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Nunavik

Nunavik (ᓄᓇᕕᒃ) is an area in Canada which comprises the northern third of the province of Quebec, part of the Nord-du-Québec region and nearly coterminous with Kativik. Covering a land area of 443,684.71 km2 north of the 55th parallel, it is the homeland of the Inuit of Quebec and part of the wider Inuit Nunangat. Almost all of the 14,045 inhabitants (2021 census) of the region, of whom 90% are Inuit, live in fourteen northern villages on the coast of Nunavik and in the Cree reserved land (TC) of Whapmagoostui, near the northern village of Kuujjuarapik.

Nunavik means "great land" in the local dialect of Inuktitut and the Inuit inhabitants of the region call themselves Nunavimmiut. Until 1912, the region was part of the District of Ungava of the Northwest Territories.

Negotiations for regional autonomy and resolution of outstanding land claims took place in the 2000s. The seat of government would be Kuujjuaq. Negotiations on better empowering Inuit political rights in their land are still ongoing.

A flag for Nunavik was proposed by Nunavik artist and graphic designer Thomassie Mangiok during an April 2013 Plan Nunavik consultation in Ivujivik.

History
Concern about Canada's claims to sovereignty in the high Arctic resulted in the high Arctic relocation, where the federal government of Canada forced several Inuit families to leave Nunavik in the 1950s. They were transported much further north, to barren hamlets at Grise Fiord and Resolute in what is now Nunavut in an effort to demonstrate Canada's legal occupation of these territories and thereby assert sovereignty in the high Arctic by increasing its population during the Cold War. Eight Inuit families from Inukjuak (on the Ungava Peninsula) were relocated after being promised homes and game to hunt, but the relocated people discovered no buildings and very little familiar wildlife. They were told that they would be returned home to Nunavik after a year if they wished, but this offer was later withdrawn as it would damage Canada's claims to sovereignty in the High Arctic area and the Inuit were forced to stay. Eventually, the Inuit learned the local beluga whale migration routes and were able to survive in the area, hunting over a range of 18,000 km2 each year.

In 1993, the Canadian government held hearings to investigate the relocation program. The Royal Commission on Aboriginal Peoples issued a report the following year entitled The High Arctic Relocation: A Report on the 1953–55 Relocation. The government paid $10 million CAD to the survivors and their families, and finally apologized in 2010. The whole story is told in Melanie McGrath's The Long Exile: A Tale of Inuit Betrayal and Survival in the High Arctic.

Nunavik and other parts of northern Quebec were part of Northwest Territories from 1870 to 1912. In 1912, the area was transferred to Quebec; however, the province did little in the area until after the Quiet Revolution in the 1960s. In the 1960s, René Lévesque played a major role in expansion of hydroelectric power in the province. The region was named "Nouveau-Québec", many place names were francized, and the teaching of French was spread in schools in the region. This cultural encroachment paired with the James Bay Project resulted in the first political organizing of Inuit in Canada in the Northern Quebec Inuit Association which fought for the eventual James Bay and Northern Quebec Agreement. This agreement laid the initial legal groundwork for the creation of Nunavik within Quebec.

Geography
Nunavik is a vast territory located in the northernmost part of Quebec. It lies in both the Arctic and subarctic climate zones. All together, about 12,000 people live in Nunavik's communities, and this number has been growing in line with the tendency for high population growth in indigenous communities.

Nunavik is separated from the territory of Nunavut by Hudson Bay to the west and Hudson Strait and Ungava Bay to the north. Nunavik shares a border with the Côte-Nord region of Quebec and the Labrador region of the province of Newfoundland and Labrador. The Ungava Peninsula forms the northern two-thirds of the region. There are no road links between Nunavik and southern Quebec, although the Trans-Taiga Road of the Jamésie region ends near the 55th parallel on the Caniapiscau Reservoir, several hundred kilometres south of Kuujjuaq. There is a year-round air link to all villages and seasonal shipping in the summer and autumn. Parts of the interior of southern Nunavik can be reached using several trails which head north from Schefferville. Nunavik has fourteen villages, the vast majority of whose residents are Inuit. The principal village and administrative centre in Nunavik is Kuujjuaq, on the southern shore of Ungava Bay; the other villages are Inukjuak (where the film Nanook of the North was shot), Salluit, Puvirnituq, Ivujivik, Kangiqsujuaq, Kangiqsualujjuaq, Kangirsuk, Tasiujaq, Aupaluk, Akulivik, Quaqtaq, Kuujjuarapik and Umiujaq. The village population (census 2011) ranges from 2,375 (Kuujjuaq) to 195 (Aupaluk).

There are five meteorite craters in Nunavik: Pingualuit crater, Couture crater, La Moinerie crater and the two craters that together form the Clearwater Lakes.

Climate
Nunavik is dominated by tundra, which is characterized by its limited vegetation and low temperatures. Nunavik's climate features long and cold winters as the seas to the west, east and north freeze over, eliminating maritime moderation. Since this moderation exists in summer when the surrounding sea thaws, even those temperatures are subdued. Inukjuak for example has summer highs averaging just 13 °C (55 °F) with January highs of −21 °C (−6 °F). This is exceptionally cold for a sea-level settlement more than 1/3 of the way from the North Pole to the Equator. Annual temperatures are up to 15 °C (27 °F) colder than marine areas of Northern Europe on similar parallels. Areas less affected by summertime marine moderation have somewhat warmer temperatures and unlike the west coast, feature marginal taiga due to summers being warmer than 10 °C (50 °F) in mean temperatures.

Climate change and environment
Climate change studies in Nunavik have employed community-based research methods, synthesizing traditional ecological knowledge (TEK) and quantitative data, and provide new insights into observable changes occurring in the Arctic. Indigenous communities have reported shorter, warmer winters in recent years, and have observed resulting changes in various environmental factors – including vegetation growth, precipitation, sea ice and permafrost, water levels and quality, as well as the presence of lead in the environment.

Vegetation growth is limited in Nunavik, mostly consisting of shrubs, grasses, and mosses. Although tree growth in the tundra is scarce, some tree species such as the Arctic Willow and Balsam Poplar are found in this region. Nunavik is also home to a variety of berry plants, including Cloudberry, Blueberry, Blackberry (Crowberry), and Cranberry (Redberry). Tree and shrub growth has been observed to be increasing in Nunavik in past years due to warming temperatures.

Furthermore, sea ice is thinning and decreasing in longevity through the winters. This creates more risky areas for transportation over the ice. There have also been lowering fresh water levels reported due to decreasing annual precipitation in the Arctic.

These changes are presenting potential threats to the health of communities and people that use water from natural sources. Lowering water quality in Nunavik can be associated with Gastrointestinal diseases, for example Giardia. Cases of Gastrointestinal diseases associated with natural sources were reported to increase in March when the sea ice begins breaking up, as well as in fall during the Caribou migration period.

Environmental levels of lead have also been changing in the Arctic with climatic shifts, presenting concerns for lead poisoning in northern communities. In Nunavik, Lead concentrations in maternal blood were the highest in Canada (50 μg/L). Increasing levels of lead in the environment are also associated with the use of the lead shot in hunting, which was banned in 1999 (although lead shots continue to be shipped to northern communities).

Ethnicity
In 2019, a scientific study by researchers from the Montreal Neurological Institute and Hospital of the McGill University found that the Nunavik Inuit are genetically distinct from any other known population. They possess distinct genetic signatures in pathways linked to lipid metabolism, allowing them to adjust to higher-fat diets and the extreme temperature of the Canadian Arctic. Geographically isolated populations often develop unique genetic traits that result from their successful adaptation to specific environments. Their closest relatives are the Paleo-Eskimos, a people that inhabited the Arctic before the Inuit.

Language
The following table does not include Canada's official languages of French and English.

Economy
Nunavik is rich in mineral deposits where Raglan Mine, situated near Salluit, is one of the largest mines in the region. It is linked by all-weather roads to an airstrip at Kattiniq/Donaldson Airport and to the concentrate, storage and ship-loading facilities at Deception Bay. Production began at the mine in 1997. The current mine life is estimated at more than 30 years.

Because the site is situated in the subarctic permafrost region, it requires special construction and mining techniques to protect the fragile permafrost and to address other environmental issues. The average annual temperature is -10 C with an average ambient temperature underground of -15 C. There are plans to increase production at a new mine in Raglan South.

Arts and culture
The villages of Nunavik are populated predominately by Inuit. Much like their Nunavummiut neighbours to the North, the Nunavimmiut carve sculptures from soapstone and eat primarily caribou and fish. On clear nights, the aurora is often visible, and outdoors activities are abundant in this region.

Government
Nunavik, along with the Quebec portion of the James Bay region (or Jamésie in French), is part of the administrative region of Nord-du-Québec. The James Bay and Northern Quebec Agreement of 1978 led to greater political autonomy for most of the Nunavik region with the founding of the Kativik Regional Government. All inhabitants of the 14 northern villages, both Inuit and non-Inuit, vote in regional elections. The Kativik Regional Government is financed by the Government of Quebec (50%), the Government of Canada (25%), and local revenues (25%). The Agreement also led to the creation of the Kativik Regional Police Force, which has been providing police services in the Kativik region since 1996. The KRPF was renamed as the Nunavik Police Service (NPS) in mid-2021.

The Makivik Corporation, headquartered in Kuujjuaq, represents the Inuit of Northern Quebec in their relations with the governments of Quebec and Canada. They are seeking greater political autonomy for the region and have recently negotiated an agreement defining their traditional rights to use the resources of the offshore islands of Nunavik, all of which are part of Nunavut.

The Cree village of Whapmagoostui, which forms an enclave on the eastern shore of Hudson Bay near the northern village of Kuujjuarapik, is part of the Cree Regional Authority, which itself has been incorporated into the Grand Council of the Crees (Eeyou Istchee). The Naskapi Nation of Kawawachikamach, of the Côte-Nord region to the south of Nunavik, owns an exclusive hunting and trapping area in southern Nunavik and is represented in the Kativik Regional Government.

Regional Government of Nunavik
The governments of Quebec and Canada and Nunavik had negotiated a proposal to establish a Regional Government of Nunavik. This is in part a recognition of the region's political distinctiveness, having a different language, culture, climate and voting pattern from the rest of the province of Quebec, as well as part of the overall trend towards devolution of Canada's arctic territories. While Quebec and Canada would still maintain full jurisdiction over the area, the Nunavik government will have an elected parliamentary-style council and cabinet, and a public service funded by the province and responsible for delivering certain social services such as education and health. The regional government would have also had rights to the region's natural resources, including royalties from the various mines in the region. This proposal was rejected by about 66% of voters in a referendum in 2011. It is expected that negotiations will continue in the future to work to establish a more autonomous government for Nunavik in the future.

The government will be based on territory, not ethnicity, so that all people residing in Nunavik can be full participants. Existing government structures, such as the Kativik Regional Government, Kativik School Board, and Nunavik Regional Board of Health and Social Services, will be folded into the new regional government.

The Quebec government has also expressed a desire to add an additional seat to the National Assembly to represent Nunavik, despite the region's small population. Currently, Nunavik is part of the riding of Ungava, its residents making up just under half of the riding's population. As a riding, Nunavik would be the second least populous in Quebec, slightly more populous than Îles-de-la-Madeleine, which is able to exist as a separate riding under an exception to the laws on population distribution by riding.

title: Nunavik


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John George Hohman

John George Hohman (also spelled Johann Georg Hohman, and his surname sometimes misspelled as Hoffman) was a German-American printer, book seller and compiler of collections of herbal remedies, magical healings, and charms. He immigrated to the USA from Germany in 1802, settled in the area around Reading, Pennsylvania, in the Pennsylvania Dutch community, where he printed and sold broadsides, chapbooks and books and practised and instructed in the arts of folk magic and folk religion which became known as pow-wow. He was active between 1802 and 1846.

Hohman's best known work is the collection of prayers and recipes for folk-healing titled Pow-Wows, or the Long Lost Friend, published in German in 1820 as Der Lange Verborgene Freund (The Long-Hidden Friend) and in two English translations—the first in 1846 in a rather crude translation by Hohman himself ("The Long Secreted Friend or a True and Christian Information for Every Body") and the second in 1856 by a different and more fluent translator ("The Long Lost Friend; a Collection of Mysterious and Invaluable Arts and Remedies for Man as well as Animals"). The name "Pow-Wows" was only added to the book in late 19th century reprints in the wake of the sudden popularity of Spiritualism in the United States, in which "Indian Spirit Guides" were frequently seen during seances.

In addition to "The Long-Lost-Friend," Hohman also wrote and published, or at least had attributed to him, a number of further books in German, including Unsers Herran Jesu Christi Kinderbuch, oder, Merkwurdige Historische Beschreibung Von Joachim Und Anna (Our Lord Jesus Christ's Childhood-Book, or, The Strange Historical Description of Joachim and Anna), and Albertus Magnus, oder, Der Lange Verborgene und Getreuer und Christlicher Unterricht fur Jedermann (Albertus Magnus, or, Long Lost and True and Christian Instructions for Everyone). The last book attributed to Hohman was published in 1857.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: John George Hohman


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Attractor

In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.

In finite-dimensional systems, the evolving variable may be represented algebraically as an n-dimensional vector. The attractor is a region in n-dimensional space. In physical systems, the n dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; in economic systems, they may be separate variables such as the inflation rate and the unemployment rate.

If the evolving variable is two- or three-dimensional, the attractor of the dynamic process can be represented geometrically in two or three dimensions, (as for example in the three-dimensional case depicted to the right). An attractor can be a point, a finite set of points, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor (see strange attractor below). If the variable is a scalar, the attractor is a subset of the real number line. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.

A trajectory of the dynamical system in the attractor does not have to satisfy any special constraints except for remaining on the attractor, forward in time. The trajectory may be periodic or chaotic. If a set of points is periodic or chaotic, but the flow in the neighborhood is away from the set, the set is not an attractor, but instead is called a repeller (or repellor).

Motivation of attractors
A dynamical system is generally described by one or more differential or difference equations. The equations of a given dynamical system specify its behavior over any given short period of time. To determine the system's behavior for a longer period, it is often necessary to integrate the equations, either through analytical means or through iteration, often with the aid of computers.

Dynamical systems in the physical world tend to arise from dissipative systems: if it were not for some driving force, the motion would cease. (Dissipation may come from internal friction, thermodynamic losses, or loss of material, among many causes.) The dissipation and the driving force tend to balance, killing off initial transients and settle the system into its typical behavior. The subset of the phase space of the dynamical system corresponding to the typical behavior is the attractor, also known as the attracting section or attractee.

Invariant sets and limit sets are similar to the attractor concept. An invariant set is a set that evolves to itself under the dynamics. Attractors may contain invariant sets. A limit set is a set of points such that there exists some initial state that ends up arbitrarily close to the limit set (i.e. to each point of the set) as time goes to infinity. Attractors are limit sets, but not all limit sets are attractors: It is possible to have some points of a system converge to a limit set, but different points when perturbed slightly off the limit set may get knocked off and never return to the vicinity of the limit set.

For example, the damped pendulum has two invariant points: the point $x_{0}$ of minimum height and the point $x_{1}$ of maximum height. The point $x_{0}$ is also a limit set, as trajectories converge to it; the point $x_{1}$ is not a limit set. Because of the dissipation due to air resistance, the point $x_{0}$ is also an attractor. If there was no dissipation, $x_{0}$ would not be an attractor. Aristotle believed that objects moved only as long as they were pushed, which is an early formulation of a dissipative attractor.

Some attractors are known to be chaotic (see strange attractor), in which case the evolution of any two distinct points of the attractor result in exponentially diverging trajectories, which complicates prediction when even the smallest noise is present in the system.

Mathematical definition
Let $$t$$ represent time and let $$f(t,\cdot)$$ be a function which specifies the dynamics of the system. That is, if $$a$$ is a point in an $$n$$-dimensional phase space, representing the initial state of the system, then $$f(0,a)=a$$ and, for a positive value of $$t$$, $$f(t,a)$$ is the result of the evolution of this state after $$t$$ units of time. For example, if the system describes the evolution of a free particle in one dimension then the phase space is the plane $$\R^2$$ with coordinates $$(x,v)$$, where $$x$$ is the position of the particle, $$v$$ is its velocity, $$a=(x,v)$$, and the evolution is given by

 * $$ f(t,(x,v))=(x+tv,v).\ $$

An attractor is a subset $$A$$ of the phase space characterized by the following three conditions:
 * $$A$$ is forward invariant under $$f$$: if $$a$$ is an element of $$A$$ then so is $$f(t,a)$$, for all $$t>0$$.
 * There exists a neighborhood of $$A$$, called the basin of attraction for $$A$$ and denoted $$B(A)$$, which consists of all points $$b$$ that "enter" $$A$$ in the limit $$t\to\infty$$. More formally, $$B(A)$$ is the set of all points $$b$$ in the phase space with the following property:
 * For any open neighborhood $$N$$ of $$A$$, there is a positive constant $$T$$ such that $$f(t,b)\in N$$ for all real $$t>T$$.

 * There is no proper (non-empty) subset of $$A$$ having the first two properties.

Since the basin of attraction contains an open set containing $$A$$, every point that is sufficiently close to $$A$$ is attracted to $$A$$. The definition of an attractor uses a metric on the phase space, but the resulting notion usually depends only on the topology of the phase space. In the case of $$\R^n$$, the Euclidean norm is typically used.

Many other definitions of attractor occur in the literature. For example, some authors require that an attractor have positive measure (preventing a point from being an attractor), others relax the requirement that $$B(A)$$ be a neighborhood.

Types of attractors
Attractors are portions or subsets of the phase space of a dynamical system. Until the 1960s, attractors were thought of as being simple geometric subsets of the phase space, like points, lines, surfaces, and simple regions of three-dimensional space. More complex attractors that cannot be categorized as simple geometric subsets, such as topologically wild sets, were known of at the time but were thought to be fragile anomalies. Stephen Smale was able to show that his horseshoe map was robust and that its attractor had the structure of a Cantor set.

Two simple attractors are a fixed point and the limit cycle. Attractors can take on many other geometric shapes (phase space subsets). But when these sets (or the motions within them) cannot be easily described as simple combinations (e.g. intersection and union) of fundamental geometric objects (e.g. lines, surfaces, spheres, toroids, manifolds), then the attractor is called a strange attractor.

Fixed point
A fixed point of a function or transformation is a point that is mapped to itself by the function or transformation. If we regard the evolution of a dynamical system as a series of transformations, then there may or may not be a point which remains fixed under each transformation. The final state that a dynamical system evolves towards corresponds to an attracting fixed point of the evolution function for that system, such as the center bottom position of a damped pendulum, the level and flat water line of sloshing water in a glass, or the bottom center of a bowl containing a rolling marble. But the fixed point(s) of a dynamic system is not necessarily an attractor of the system. For example, if the bowl containing a rolling marble was inverted and the marble was balanced on top of the bowl, the center bottom (now top) of the bowl is a fixed state, but not an attractor. This is equivalent to the difference between stable and unstable equilibria. In the case of a marble on top of an inverted bowl (a hill), that point at the top of the bowl (hill) is a fixed point (equilibrium), but not an attractor (unstable equilibrium).

In addition, physical dynamic systems with at least one fixed point invariably have multiple fixed points and attractors due to the reality of dynamics in the physical world, including the nonlinear dynamics of stiction, friction, surface roughness, deformation (both elastic and plasticity), and even quantum mechanics. In the case of a marble on top of an inverted bowl, even if the bowl seems perfectly hemispherical, and the marble's spherical shape, are both much more complex surfaces when examined under a microscope, and their shapes change or deform during contact. Any physical surface can be seen to have a rough terrain of multiple peaks, valleys, saddle points, ridges, ravines, and plains. There are many points in this surface terrain (and the dynamic system of a similarly rough marble rolling around on this microscopic terrain) that are considered stationary or fixed points, some of which are categorized as attractors.

Finite number of points
In a discrete-time system, an attractor can take the form of a finite number of points that are visited in sequence. Each of these points is called a periodic point. This is illustrated by the logistic map, which depending on its specific parameter value can have an attractor consisting of 1 point, 2 points, 2n points, 3 points, 3×2n points, 4 points, 5 points, or any given positive integer number of points.

Limit cycle
A limit cycle is a periodic orbit of a continuous dynamical system that is isolated. It concerns a cyclic attractor. Examples include the swings of a pendulum clock, and the heartbeat while resting. The limit cycle of an ideal pendulum is not an example of a limit cycle attractor because its orbits are not isolated: in the phase space of the ideal pendulum, near any point of a periodic orbit there is another point that belongs to a different periodic orbit, so the former orbit is not attracting. For a physical pendulum under friction, the resting state will be a fixed-point attractor. The difference with the clock pendulum is that there, energy is injected by the escapement mechanism to maintain the cycle.

Limit torus
There may be more than one frequency in the periodic trajectory of the system through the state of a limit cycle. For example, in physics, one frequency may dictate the rate at which a planet orbits a star while a second frequency describes the oscillations in the distance between the two bodies. If two of these frequencies form an irrational fraction (i.e. they are incommensurate), the trajectory is no longer closed, and the limit cycle becomes a limit torus. This kind of attractor is called an $N_{t}$ -torus if there are $N_{t}$ incommensurate frequencies. For example, here is a 2-torus:

A time series corresponding to this attractor is a quasiperiodic series: A discretely sampled sum of $N_{t}$ periodic functions (not necessarily sine waves) with incommensurate frequencies. Such a time series does not have a strict periodicity, but its power spectrum still consists only of sharp lines.

Strange attractor
An attractor is called strange if it has a fractal structure, that is if it has non-integer Hausdorff dimension. This is often the case when the dynamics on it are chaotic, but strange nonchaotic attractors also exist. If a strange attractor is chaotic, exhibiting sensitive dependence on initial conditions, then any two arbitrarily close alternative initial points on the attractor, after any of various numbers of iterations, will lead to points that are arbitrarily far apart (subject to the confines of the attractor), and after any of various other numbers of iterations will lead to points that are arbitrarily close together. Thus a dynamic system with a chaotic attractor is locally unstable yet globally stable: once some sequences have entered the attractor, nearby points diverge from one another but never depart from the attractor.

The term strange attractor was coined by David Ruelle and Floris Takens to describe the attractor resulting from a series of bifurcations of a system describing fluid flow. Strange attractors are often differentiable in a few directions, but some are like a Cantor dust, and therefore not differentiable. Strange attractors may also be found in the presence of noise, where they may be shown to support invariant random probability measures of Sinai–Ruelle–Bowen type.

Examples of strange attractors include the double-scroll attractor, Hénon attractor, Rössler attractor, and Lorenz attractor.

Attractors characterize the evolution of a system

The parameters of a dynamic equation evolve as the equation is iterated, and the specific values may depend on the starting parameters. An example is the well-studied logistic map, $$x_{n+1}=rx_n(1-x_n)$$, whose basins of attraction for various values of the parameter $$r$$ are shown in the figure. If $$r=2.6$$, all starting $$x$$ values of $$x<0$$ will rapidly lead to function values that go to negative infinity; starting $$x$$ values of $$x>1$$ will also go to negative infinity. But for $$0<x<1$$ the $$x$$ values rapidly converge to $$x\approx0.615$$, i.e. at this value of $$r$$, a single value of $$x$$ is an attractor for the function's behaviour. For other values of $$r$$, more than one value of $$x$$ may be visited: if $$r$$ is 3.2, starting values of $$0<x<1$$ will lead to function values that alternate between $$x\approx0.513$$ and $$x\approx0.799$$. At some values of $$r$$, the attractor is a single point (a "fixed point"), at other values of $$r$$ two values of $$x$$ are visited in turn (a period-doubling bifurcation), or, as a result of further doubling, any number $$k\times 2^n$$ values of $$x$$; at yet other values of $$r$$, any given number of values of $$x$$ are visited in turn; finally, for some values of $$r$$, an infinitude of points are visited. Thus one and the same dynamic equation can have various types of attractors, depending on its starting parameters.

Basins of attraction
An attractor's basin of attraction is the region of the phase space, over which iterations are defined, such that any point (any initial condition) in that region will asymptotically be iterated into the attractor. For a stable linear system, every point in the phase space is in the basin of attraction. However, in nonlinear systems, some points may map directly or asymptotically to infinity, while other points may lie in a different basin of attraction and map asymptotically into a different attractor; other initial conditions may be in or map directly into a non-attracting point or cycle.

Linear equation or system
An univariate linear homogeneous difference equation $$x_t=ax_{t-1}$$ diverges to infinity if $$|a|>1$$ from all initial points except 0; there is no attractor and therefore no basin of attraction. But if $$|a|<1$$ all points on the number line map asymptotically (or directly in the case of 0) to 0; 0 is the attractor, and the entire number line is the basin of attraction.

Likewise, a linear matrix difference equation in a dynamic vector $$X$$, of the homogeneous form $$X_t=AX_{t-1}$$ in terms of square matrix $$A$$ will have all elements of the dynamic vector diverge to infinity if the largest eigenvalues of $$A$$ is greater than 1 in absolute value; there is no attractor and no basin of attraction. But if the largest eigenvalue is less than 1 in magnitude, all initial vectors will asymptotically converge to the zero vector, which is the attractor; the entire $$n$$-dimensional space of potential initial vectors is the basin of attraction.

Similar features apply to linear differential equations. The scalar equation $$ dx/dt =ax$$ causes all initial values of $$x$$ except zero to diverge to infinity if $$a>0$$ but to converge to an attractor at the value 0 if $$a<0$$, making the entire number line the basin of attraction for 0. And the matrix system $$dX/dt=AX$$ gives divergence from all initial points except the vector of zeroes if any eigenvalue of the matrix $$A$$ is positive; but if all the eigenvalues are negative the vector of zeroes is an attractor whose basin of attraction is the entire phase space.

Nonlinear equation or system
Equations or systems that are nonlinear can give rise to a richer variety of behavior than can linear systems. One example is Newton's method of iterating to a root of a nonlinear expression. If the expression has more than one real root, some starting points for the iterative algorithm will lead to one of the roots asymptotically, and other starting points will lead to another. The basins of attraction for the expression's roots are generally not simple—it is not simply that the points nearest one root all map there, giving a basin of attraction consisting of nearby points. The basins of attraction can be infinite in number and arbitrarily small. For example, for the function $$f(x)=x^3-2x^2-11x+12$$, the following initial conditions are in successive basins of attraction:

 * 2.35287527 converges to 4;
 * 2.35284172 converges to −3;
 * 2.35283735 converges to 4;
 * 2.352836327 converges to −3;
 * 2.352836323 converges to 1.

Newton's method can also be applied to complex functions to find their roots. Each root has a basin of attraction in the complex plane; these basins can be mapped as in the image shown. As can be seen, the combined basin of attraction for a particular root can have many disconnected regions. For many complex functions, the boundaries of the basins of attraction are fractals.

Partial differential equations
Parabolic partial differential equations may have finite-dimensional attractors. The diffusive part of the equation damps higher frequencies and in some cases leads to a global attractor. The Ginzburg–Landau, the Kuramoto–Sivashinsky, and the two-dimensional, forced Navier–Stokes equations are all known to have global attractors of finite dimension.

For the three-dimensional, incompressible Navier–Stokes equation with periodic boundary conditions, if it has a global attractor, then this attractor will be of finite dimensions.

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Numerical localization (visualization) of attractors: self-excited and hidden attractors

From a computational point of view, attractors can be naturally regarded as self-excited attractors or hidden attractors. Self-excited attractors can be localized numerically by standard computational procedures, in which after a transient sequence, a trajectory starting from a point on an unstable manifold in a small neighborhood of an unstable equilibrium reaches an attractor, such as the classical attractors in the Van der Pol, Belousov–Zhabotinsky, Lorenz, and many other dynamical systems. In contrast, the basin of attraction of a hidden attractor does not contain neighborhoods of equilibria, so the hidden attractor cannot be localized by standard computational procedures. -->

title: Attractor


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Kangiqsualujjuaq

Kangiqsualujjuaq is an Inuit village located at the mouth of the George River on the east coast of Ungava Bay in Nunavik, Quebec, Canada. Its population was 956 as of the 2021 census.

The settlement's original name, Fort Severight, honoured John Severight, a North West Company man who had headed Fort Coulonge during McLean's time there. After its re-establishment, it was variously known from its location as Fort George, George's River, George River, George River Post, and Fort George River. It was also sometimes known as Port-Nouveau-Québec (French for "New Port Quebec").

The name "Kangiqsualujjuaq" (ᑲᖏᖅᓱᐊᓗᔾᔪᐊᖅ) is Inuktitut for "the very large bay". It is also sometimes spelled "Kangirsualujjuaq" (ᑲᖏᕐᓱᐊᓗᔾᔪᐊᖅ).

History
John McLean established Fort Severight for the Hudson's Bay Company in 1838. It was a bit south of the present-day town, at 58.52862°N, -65.89294°W (now marked as Illutaliviniq on topographic maps). It served as a salmon and seal fishery, supplying Fort Chimo to the west and Fort Trial and Fort Nascopie to the south. It was abandoned in 1842 after Fort Chimo turned out to be an unprofitable station and a path was found to supply Nascopie from Fort Smith to the southeast. The Inuit of the area never settled around the post, preferring to live along the coast in summer and setting their camps about 50 km inland in winter.

The site was taken up again in September 1876, mostly to capture the local indigenous peoples' trade which had been going to the Moravians. The new buildings were built from the old. The site was abandoned again in the summer of 1878 before reopening again in 1883. It again functioned as a salmon and seal fishery for Fort Chimo, although it carried on some local trading until that was removed to Port Burwell in 1917. HBC shuttered its office in June 1952.

In 1959, local Inuit established, on their own initiative, the first co-operative in Northern Quebec for the purpose of marketing Arctic char. Construction of the village began in 1962 and Inuit began to settle there permanently. In 1963 a school, a co-operative store, and government buildings were built. In 1980, Kangiqsualujjuaq was legally established as a municipality.

The community was struck by an avalanche in the early morning of January 1, 1999, which destroyed the Satuumavik School gymnasium during New Year celebrations, killing nine. Another 25 people were injured, 12 of them seriously enough to have to be airlifted 1,500 km to Montreal for treatment. Some speculated that it may have been triggered by lively dancing at the party. The school was rebuilt on the new, safer location and renamed to Ulluriaq School.

Geography
Kangiqsualujjuaq is located 1688 km to the northeast of Montreal. Enveloped by mountains, the township is framed by picturesque surroundings and its elevated position affords unobstructed views of the George River. The town itself is laid out on a grid pattern over levelled-ground, with two unsealed roads leading a few kilometres beyond the mountain ridges at either end of the village. Amidst rocky outcrops and stone way-finding markers (Inukshuk), the village landscape is dotted with stands of stunted trees and prostrate groundcover that clings perilously to the rugged granite terrain. In low-lying areas, the ground is covered by thick carpets of moss and lichen.

Demographics
In the 2021 Census of Population conducted by Statistics Canada, Kangiqsualujjuaq had a population of $956$ living in $247$ of its $270$ total private dwellings, a change of NaN% from its 2016 population of $942$. With a land area of 34.33 km2, it had a population density of in 2021.

Economy
Industries in Kangiqsualujjuaq include hunting of caribou, seal and beluga whale, Arctic char fishing, and the production of Inuit art. The town is also the main terminus of the George River canoeing expeditions (e.g. one of Chewonki Foundation's canoe trips).

Government
The police services are provided by the Kativik Regional Police Force. The Kativik School Board formerly operated the Ulluriaq School, previously the Satuumavik School.

Infrastructure
The town is served by the small Kangiqsualujjuaq Airport. Access is usually by plane, although Kangiqsualujjuamiut occasionally travel to Kuujjuaq in winter by snowmobile and in summer by boat, a journey of approximately 160 km to the southwest. Journeys across the Torngat Mountains by snowmobile to the Labrador settlements Nain and Nachvak are rarely embarked upon these days, but were commonplace when dog teams were used. Cargo ships from Becancour deliver cumbersome supplies and equipment to the community every summer.

Notable people

 * Mary Simon (Ningiukadluk), 30th Governor General of Canada
 * Donat Savoie

Inuit elders from Kangiqsualujjuaq include:
 * Noah Angnatuk
 * George Annanack
 * Johnny Sam Annanack
 * Maggie Annanack (Elsie Imaq)
 * Sarah Annanack
 * Willie Emudluk
 * Tivi Etok
 * Willie Etok
 * Benjamin Jararuse

Explorers and missionaries who have visited the town include:
 * Mina Benson Hubbard
 * George Kmoch
 * Benjamin Gottlieb Kohlmeister
 * Albert Peter Low
 * John McLean

title: Kangiqsualujjuaq


text:
William Lloyd Webber

William Southcombe Lloyd Webber (11 March 1914 – 29 October 1982) was an English organist and composer, who achieved some fame as a part of the modern classical music movement whilst commercially facing mixed opportunities. Besides his long and prestigious career, composing works ranging from choral pieces to instrumental items and more, he is known for being the father of both fellow composer Andrew Lloyd Webber and virtuoso cellist Julian Lloyd Webber. He also notably served as a teacher, instructing pupils on music theory at the Royal College of Music for many years until his death in 1982.

Childhood
Webber was born in London. The son of William Charles Henry Webber, a self-employed plumber, he was fortunate that his father was a keen organ 'buff' who spent what little money he had travelling to hear various organs in and around the capital. Often he would take his son with him and, before long, young William started to play the organ himself and developed a keen interest that bordered on the obsessional.

By the age of 14, William Lloyd Webber had already become a well-known organ recitalist, giving frequent performances at many churches and cathedrals throughout Great Britain. He won an organ scholarship to the Mercers' School, later winning a further scholarship to study at the Royal College of Music, where he studied with Ralph Vaughan Williams and gained his FRCO diploma at nineteen. Because there was already another student at the college with the name William Webber, William continued to use his second middle name 'Lloyd' from then on as part of his last name.

Prolific years
Lloyd Webber's earliest known composition is the "remarkably assured" Fantasy Trio in B minor for violin, cello and piano of 1936 (which didn't receive its premiere until 1995). In 1938, he was appointed organist and head of the choir school at All Saints, Margaret Street, in the Marylebone district of London. He later became musical director at Westminster Central Hall, London, the headquarters of the Methodist church in the United Kingdom. His first compositions developed in the 1930s. In 1942 he married the pianist and violinist Jean Hermione Johnstone (1921–1993). The marriage, which lasted until his death, produced two sons: composer Andrew (born 1948) and cellist Julian (born 1951).

From 1945 until the 1960s, Lloyd Webber composed vocal and instrumental music, choral and organ works, chamber music and orchestral works. Compositions from this period include the oratorio St. Francis of Assisi (1948), the orchestral tone-poem Aurora (1948), and the six Country Impressions (1960), each movement for a solo woodwind instrument and piano. There are also sonatinas for viola and flute, numerous songs, organ pieces and choral works. But Webber's roots were firmly embedded in the romanticism of such composers as Sergei Rachmaninov, Jean Sibelius and César Franck, and he became increasingly convinced that his own music was 'out of step' with the prevailing climate of the time. Rather than compromise his style, he turned to the academic side of British musical life. He taught at the Royal College of Music, directed the choir of Westminster Central Hall, and in 1964 was appointed Director of the London College of Music, a post which he held until his death in 1982.

Orchestra

 * Lento in E major for string orchestra (1939)
 * Waltz in E minor for orchestra (1939)
 * Aurora, Tone Poem for orchestra (1948)
 * Three Spring Miniatures for small orchestra (1952); orchestration of original piano work
 * Gossamer (A Little Waltz)
 * Willow Song (A lament)
 * Tree Tops (A Toccatina)

 * Serenade for Strings for string orchestra
 * I. Barcarolle (1951)
 * II. Romance (1980)
 * III. Elegy (1960)

 * Invocation for harp, timpani and string orchestra (1957)

Brass band

 * Little Suite for brass
 * I. Prelude
 * II. Adagio
 * III. Festival March

Chamber music

 * Three Pieces for cello and piano
 * In the Half-Light (1951)
 * Air Varié (adapted from Tantum Ergo by César Franck)
 * Slumber Song

 * Fantasy Trio in B minor for violin, cello and piano (1936)
 * Sonatina for flute and piano (1941)
 * Benedictus for violin and organ (1942)
 * Nocturne for cello and piano or harp (1948); from the oratorio St. Francis of Assisi
 * Sonatina for viola and piano (1951)
 * Air and Variations for clarinet and piano (1952)
 * Suite in B♭ for trumpet and piano (1952)
 * Country Impressions (1960)
 * Mulberry Cottage for flute and piano (1960)
 * On Frensham Pond, Aquarelle for clarinet and piano (1960)

 * A Lyric Suite for cello and piano (1964)
 * Summer Pastures for horn and piano
 * The Gardens at Eastwell, A Late Summer Impression for violin and piano or harp (1982)

Choral

 * Missa Sanctae Mariae Magdalenae for choir and organ (1979)
 * Missa Princeps Pacis (The Prince of Peace), mass for chorus and organ (1962)
 * The Saviour (cantata), A Meditation upon the Death of Christ for chorus and organ
 * The Divine Compassion, Sacred Cantata for tenor, baritone, chorus and organ
 * St. Francis of Assisi, Oratorio for soprano, tenor, baritone, chorus, string orchestra and harp (1948)
 * Born a King, a Christmas cantata for soloists, chorus and organ
 * Songs of Spring, Cantata for female chorus and piano
 * O Lord, Spread Thy Wings O'er Me, Anthem for soprano (or treble voice), chorus and accompaniment
 * Spirit of God, Anthem for chorus and organ
 * Dominus Firmamentum Meum, Anthem for chorus and organ
 * Lo! My Shepherd Is Divine, Anthem for soprano, alto, chorus and organ
 * Lo, God Is Here, Anthem for chorus and organ
 * Seven Anthems
 * Sing the Life, Easter Carol for chorus and accompaniment
 * A Hymn of Thanksgiving for unison voices and organ
 * O Love, I Give Myself to Thee for female chorus and organ
 * O for a Closer Walk with God for chorus and organ
 * Then Come, All Ye People, Carol for chorus and accompaniment
 * The Lord Is My Shepherd for chorus and organ
 * Love Divine, All Loves Excelling for chorus and organ (1964); from The Good Samaritan

 * Tantum Ergo, Anthem for bass solo, chorus and organ
 * Jesus, Dear Jesus, Carol for boy treble, children's choir and organ
 * The Stable Where the Oxen Stood
 * Most Glorious Lord of Lyfe, Anthem Suitable for Easter for chorus; words by Edmund Spenser
 * Meeting Place, a Meditation upon the Birth of Christ for baritone, chorus and piano or organ (1964)
 * Jamie Brown, a Happy Story in Song for two-part chorus and piano (published 1962)
 * Magnificat and Nunc Dimmitis in E minor

Partsongs
 * April for female chorus and piano
 * Corinna's Lute for female chorus and piano
 * Sun-Gold for female chorus and piano; words by May Sarson
 * Moon Silver for female chorus and piano
 * Lament for female chorus and piano
 * I heard a Rush of Wings for female (or children's) chorus and piano
 * The Moon for unaccompanied chorus
 * A Magic Morn for female chorus and piano
 * The Heather Hills for female chorus and piano

Vocal

 * The Call of the Morning (1950); words by George Darley
 * Love, Like a Drop of Dew (1950); words by W. H. Davies
 * I Looked Out into the Morning (1951); words by James Thomson (B.V.)
 * Over the Bridge (1951); words by James Thomson (B.V.)
 * How Do I Love Thee?
 * The Forest of Wild Thyme (1951)
 * The Pretty Washer-Maiden; words by William Ernest Henley
 * To the Wicklow Hills (1954); words by R.G. Leigh
 * A Rent for Love (1982); words by Irvonwy Morgan
 * So Lovely the Rose; words by Joseph Murrells
 * Eutopia; words by Francis Turner Palgrave
 * The Cottage of Dreams
 * Lullaby
 * Spring Is the Time for Love
 * Three Arias for tenor and organ
 * And I Saw a New Heaven
 * The King of Love (from The Saviour)
 * Thou Art the King (from The Divine Compassion)

Piano

 * Three Spring Miniatures (1952); also orchestrated
 * Gossamer (A Little Waltz)
 * Willow Song (A lament)
 * Tree Tops (A Toccatina)

 * Italian Idyll, 3 Piano Duets (1954)
 * Mattinata
 * Siesta
 * Napolitana

 * Six Pieces
 * A Song for the Morning (1957); composed under the pseudonym Clive Chapel
 * Scherzo in G minor
 * Arabesque
 * Romantic Evening
 * Explanation; composed under the pseudonym Clive Chapel
 * Song without Words

 * Three Pieces
 * Presto for Perseus
 * Autumn Elf
 * Badinage de Noël

 * Scenes from Childhood
 * Cake Walk
 * Sentimental Waltz
 * Air
 * Scherzo
 * Evening Hymn
 * China Doll

 * A Short Tone-Study
 * River Song for piano 4-hands
 * Danse Macabre for 2 pianos

Organ

 * Chorale, Cantilena and Finale
 * Three Recital Pieces (1952)
 * Prelude
 * Barcarolle
 * Nuptial March

 * Aria, 13 Pieces
 * Prelude on St Cross
 * Choral March
 * Communion
 * Solemn Procession
 * Prelude on Passion Chorale
 * Prelude on Rockingham
 * Festal March
 * Prelude on Gerontius
 * Aria
 * Verset
 * Prelude on Winchester New
 * Vesper Hymn
 * Meditation on Stracathro

 * Reflections, 7 Pieces
 * Prelude
 * Slumber Song
 * Summer Pastures
 * Romance
 * Intermezzo
 * Christ in the Tomb (from The Divine Compassion)
 * Postlude

 * Eight Varied Pieces
 * Arietta in A major
 * Minuet
 * Recessional
 * Andantino alla Cantilena
 * Introit
 * Dedication March
 * Pastorale
 * Epilogue

 * Songs without Words, 6 Pieces
 * Noel Nouvelet
 * Song without Words
 * Trumpet Minuet
 * God Rest You Merry, Gentlemen
 * The Coventry Carol
 * Good King Wenceslas

 * Five Portraits for home organs
 * Elegy
 * Six Interludes on Christmas Carols
 * Interlude on 'The Holly and the Ivy'
 * Interlude on 'Whence is this goodly fragrance?'
 * Interlude on 'Noël nouvelet'
 * Interlude on 'Good King Wenceslas'
 * Interlude on 'Coventry Carol'
 * Interlude on 'God Rest You Merry, Gentlemen'

 * Rhapsody on "Helmsley"
 * Four Epilogues (for Frederick Geoghegan) (1953)
 * I. Allegro moderato
 * II. Risoluto
 * III. (Resurgam) Andante elegiaco
 * IV. Maestoso, ma con anima

 * ''Suite in B-flat Major for Organ" (To Frank Netherwood) (1951)
 * I. Prelude
 * II. Fugal Allegro
 * III. Minuet
 * IV. Choral Song

 * Six Interludes on Passion Hymns (out-of-print, Novello)

Discography

 * Music of William Lloyd Webber, (ASV Digital, CD DCA 961, 1996)
 * Organ Works of William Lloyd Webber, (Priory, PRCD 616, 1998)
 * William Lloyd Webber piano music, chamber music and songs, (Hyperion, CDA67008, 1998)
 * Sacred Choral Music of William Lloyd Webber, (Priory PRCD677, 1999)
 * Invocation, (Chandos CHAN 9595, 1998)

title: William Lloyd Webber


text:
User:The Epopt/Datebot Test

I was born on 28 March 1959. My birthday is 28 March. I was not born on 28 March 1959 BC. I certainly wasn't born on 28 March 1959 BC, 'cause I hate those periods. February 2003 may be a link, but it's not a date.

 * Is today March 10, or 10 March? I'm sure it isn't April -21, and it's probably not -21 April, either. I suppose it's not March 11.319 yet. When will it be 31 Feburary or Feburary 31? It was March IX, 2003 A.D. yesterday. It was also March 3+7, 2003 AD. April fools day is 01 April or April 01. It is March 1O today. Mach 10 is very fast. Tomorrow is Voyager 2, 3005 B.C.. The world will end on December 1e99, 1e99 BC, or maybe on March 0x1A and March 017 and March 1000000000000000000000000000000000000, 1 B.C.. كسيپ Cyp 16:29 Mar 10, 2003 (UTC)

Here is some sample code:. Did that work?

title: User:The Epopt/Datebot Test


text:
Mary Pope Osborne

Mary Pope Osborne (born May 20, 1949) is an American author of children's books and audiobook narrator. She is best known as the author of the Magic Tree House series, which sold more than 134 million copies worldwide. Both the series and Osborne have won awards, including for Osborne's charitable efforts at promoting children's literacy. One of four children, Osborne moved around in her childhood before attending the University of North Carolina. Following college, Osborne traveled before moving to New York City. She somewhat spontaneously began to write, and her first book was published in 1982. She went on to write a variety of other children's and young adult books before starting the Magic Tree House series in 1992. Osborne's sister Natalie Pope Boyce has written several compendium books to the Magic Tree House series, sometimes with Osborne's husband Will.

Childhood
Mary Pope Osborne grew up in a military family, alongside her sister, Natalie Pope Boyce, her twin brother, Bill, and younger brother, Michael. Her father's career required the family to travel rather extensively and regularly move. As a child, Osborne lived in Salzburg, Austria, as well as Oklahoma and Virginia. Osborne herself says of the experience: "Moving was never traumatic for me, but staying in one place was.” After her father retired, her family settled in a small town in North Carolina. Osborne grew invested in the local community theater, spending all her free time there.

College years, traveling, and early career
Mary Pope Osborne initially studied drama at the University of North Carolina; In her junior year, however, she switched to a major in religion with a focus on comparative religions. After graduating from UNC in 1971, Osborne and a friend went traveling. For six weeks, she camped out in a cave on the island of Crete. Following this, Osborne joined a small group of Europeans heading to the East. Their journey took Osborne through eleven countries throughout Asia, including Iraq, Iran, India, Nepal, Afghanistan, Turkey, Lebanon, Syria, and Pakistan. The trip came to an end when Osborne experienced blood poisoning requiring her to stay in a hospital for a couple of weeks where she read The Lord of the Rings. Remarking on her travels Osborne said, ""That journey irrevocably changed me. The experience was gathered that serves as a reference point every day of my life. I encountered worlds of light and worlds of darkness--and planted seeds of the imagination that led directly to my being an author of Adult's books."

After her travels, Osborne lived in California, Washington D.C., where she met her husband Will at a theater performance, and New York, where the couple moved after getting married in 1976. During this time, she held jobs including medical assistant, travel agent, drama teacher, bartender, and as an assistant editor for a children's magazine.

Life as an author
Mary Pope Osborne has written over 60 children's stories, with a variety of genres and for a range of children to young adult audiences. Her books have been named to a number of the Best Books of the Year Lists, including, School Library Journal, Parents’ Magazine, The Bulletin of the Center for Children's Books, and Bank Street College. She has received honors from such organizations as the National Council of Teachers of English, The Children's Book Council, and the International Reading Association. She received the 1992 Diamond State Reading Association Award, 2005 Ludington Memorial Award from the Educational Paperback Association and the 2010 Heidelberger Leander Award. She has also received awards from the Carolina Alumni Association, the Virginia Library Association and in spring 2013 she was awarded an Honorary Doctorate of Letters from the University of North Carolina at Chapel Hill.

Ms. Osborne served two separate terms as president of the Authors Guild and also chaired its Children's Book Committee. She has since traveled extensively in the states and throughout the world, visiting schools and speaking on issues related to reading and books. In 2011, she attended the International Tokyo Film Festival for the premier of the Magic Tree House anime film and visited schools in the tsunami-hit area of Japan. The film grossed 5.7 million dollars; Osborne donated all her proceeds into her educational works.

She was profiled on NBC's Rock Center with Brian Williams for her continued efforts to get books into the hands of underserved children on a Magic Tree House-themed tour bus. She spoke of the pressure she feels as an author that children look up to, "for a child to value someone who writes books is so extraordinary."

To celebrate the 20th anniversary of the Magic Tree House series in 2012, Ms. Osborne created a Magic Tree House Classroom Adventures Program. Ms. Osborne's mission with Classroom Adventures is to inspire children to read and to love reading while simultaneously helping kids to read at grade level by the end of 3rd grade. Free of charge, the program provides a set of online educational resources for teachers and allows for Title 1 schools to apply for free Magic Tree House books. Under Classroom Adventures, Ms. Osborne, in partnership with the First Book organization in Washington, D.C., has donated hundreds of thousands of Magic Tree House books to underserved schools.

Writing and publication
Osborne's travels and experiences have factored largely into her own writing, while her writing has allowed her to experience some of the thrills of traveling, as she said, "Without even leaving my home, I’ve traveled around the globe, learning about the religions of the world."

Osborne's writing career began "one day, out of the blue" when she wrote Run, Run As Fast As You Can in 1982. The book itself is semi-autobiographical in nature, according to Osborne: "The girl was a lot like me and many of the incidents in the story were similar to happenings in my childhood." The book served as the starting point for Osborne's writing career. Her early work received mixed reviews. Her work includes young adult novels, picture books, retellings of mythology and fairy tales, biographies, mysteries, a six-part series of the Odyssey, a book of American Tall Tales, and a book for young readers about the major world religions.

Osborne says that she can work on Magic Tree House up to 12 hours a day and seven days a week and has used space at shared office space, The Writer's Room. She has modeled her writing after Hemingway by trying to be simple and direct and is "noted for writing clear, lively, well-paced prose in both her stories and her informational books."

Family
Osborne was married to Will Osborne in 1976, meeting him after seeing him appear in a play. Mary has cited the key role Will plays in her writing saying, "Will has given me the support and encouragement I've needed to be a professional daydreamer - in other words, an author of children's books." Will and Mary also work with Mary's sister Natalie, on the non-fiction fact trackers. Mary notes that the three of them enjoy doing book tours together. She does not have any children, which she has explained as "I got too busy."

Her lakefront home features a treehouse.

Magic Tree House series
Mary Pope Osborne's most prolific work has been the Magic Tree House series. The series has sold more than 134 million books worldwide since its debut in 1992 and as of 2007 the series had spent a total 132 weeks on The New York Times Best Seller list. Owing to the successful sales of the books, Osborne for many years resisted efforts to commercialize the characters and books wanting them to live in the imaginations of children.

The first of the Magic Tree House books, Dinosaurs Before Dark, was published in 1992. She was initially inspired to write the books while working in a teen homeless shelter and realizing that for the teens writing themselves into stories taking place in the Himalayas or Serengeti had a major effect on them. Osborne says she tried writing the book seven different ways before finding a way that worked." It introduces the main characters of Jack and Annie, a brother and sister duo of adventurers who are transported to different areas of time thanks to the titular magic treehouse. The first book established the format for future books and introduced recurring characters Morgan le Fay and Merlin, as part of the Arthurian motifs. Osborne says she is more like Jack but wishes she was more like Annie.

Osborne tends to place small cliffhangers at the end of each chapter, which has been highlighted as one of the major reasons for the appeal of the books within their target age group. Another important factor in their success is the educational nature of the series. The books are cited for their ability to interest students in history and Osborne’s usage of vocabulary encourages young readers to learn new words and for their promoting gratitude and cross-cultural understanding in its readers.

Magic Tree House Children's Theatre
The Magic Tree House brand has taken on other forms. A full-scale musical adaptation was created by Will Osborne and Randy Court; Magic Tree House: The Musical, premiered in September 2007. Osborne hoped that it would have the same kind of kid and adult appeal as The Lion King or Mary Poppins. Based on the Magic Tree House book Christmas in Camelot, the Musical has toured nationally and had a cast album.

A planetarium show; Magic Tree House: Space Mission, also created by Will Osborne, is produced and presented exclusively at the Morehead Planetarium in Chapel Hill, North Carolina.

In 2011, Will Osborne collaborated with New Orleans composer Allen Toussaint and Ain't Misbehavin' co-creator Murray Horwitz to write A Night in New Orleans, a musical adaptation of Magic Tree House #42: A Good Night for Ghosts about the life of Louis Armstrong. The show features an ensemble cast and live jazz band. It premiered in 2012 at the New Jersey Performing Arts Center and was shown free to every Newark 4th grade student.

Magic Tree House Kids Shows are theatrical adaptations of selected titles in the Magic Tree House series designed specifically for performance by kids. To date, children's shows have been created by husband and wife playwright and composer team Randy Courts and Jenny Laird in collaboration with Will Osborne based on the following Magic Tree House books: Dinosaurs Before Dark, The Knight at Dawn, Pirates Past Noon, A Ghost Tale for Christmas Time, A Night in New Orleans, and Stage Fright on a Summer Night, a new children's show based on the life of William Shakespeare premiered at the Orlando Shakespeare Theatre in October 2017.

Film adaptation
In 2011, the series was adapted as a Japanese animated fantasy film, Magic Tree House (マジック・ツリーハウス). The film was directed by Hiroshi Nishikiori and the screenplay was based on the Japanese version of the novel series "Magic Tree House" by Ichiro Okouchi.

In 2016, Lionsgate acquired the film rights with a script by Will Osborne and Jenny Laird. The film would primarily contain plot elements from Book #29, Christmas in Camelot. As of 2021 no further news about this movie has been reported.

Other books
Mary Pope Osborne has written many books outside the Magic Tree House series.
 * Run, Run As Fast As You Can (Random House Children's Books, 1982)
 * The Deadly Power of Medusa (Scholastic, 1988), Will and Mary Pope Osborne, illustrated by Steve Sullivan
 * Jason and the Argonauts (Scholastic, 1988), Will and Mary Pope Osborne, illustrated by Steve Sullivan
 * Favorite Greek Myths (Scholastic, 1989), retold by Osborne, illustrated by Troy Howell
 * American Tall Tales (Knopf, 1991), retold by Osborne, illustrated by Michael McCurdy
 * Spider Kane and the Mystery under the May-apple (Knopf, 1992), illustrated by Victoria Chess — middle-grade chapter book, first of the Spider Kane series
 * Mermaid Tales from Around the World (Scholastic, 1993), retold by Osborne, illustrated by Troy Howell
 * Haunted Waters (Candlewick, 1994), young-adult fantasy novel
 * Favorite Norse Myths (Scholastic, 1996), retold by Osborne, illustrated by Troy Howell
 * Rocking Horse Christmas (Scholastic, 1997), illustrated by Ned Bittinger
 * Favorite Medieval Tales (Scholastic, 1998), retold by Osborne, illustrated by Troy Howell
 * Standing in the Light: The Captive Diary of Catharine Carey Logan, Delaware Valley, Pennsylvania, 1763 (Dear America series, Scholastic, 1998)
 * My Secret War: The World War II Diary of Madeline Beck (Dear America, Scholastic, 2000)
 * My Brother's Keeper (My America series, Scholastic, 2000), first of three Virginia's Civil War Diary
 * Kate and the Beanstalk (Atheneum Books, 2000), picture book illustrated by Giselle Potter — adaptation of the traditional fairy tale Jack and the Beanstalk
 * Tales from the Odyssey (Hyperion Books, 2002 to 2005), illustrated by Troy Howell — six children's novels adapted from Odyssey
 * Tales from the Odyssey (Hyperion, 2010), a two-volume edition
 * Moonhorse (Dragonfly Books, 2010), chapter book
 * Johnny Appleseed
 * The Life of Jesus in Masterpieces of Art (Viking: Penguin Putnam, 1998)

Audiobooks (Excerpt)

 * 2005: Magic Tree House Collection: Books 17-24, Random House UK Ltd, EAN 9780307245267 (read by the author)
 * 2011: Magic Tree House Collection: Books 1-8 (read by the author, Listening Library publishing & Audible)

title: Mary Pope Osborne


text:
Phase space

In dynamical systems theory and control theory, a phase space or state space is a space in which all possible "states" of a dynamical system or a control system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. It is the direct product of direct space and reciprocal space. The concept of phase space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré, and Josiah Willard Gibbs.

Principles
In a phase space, every degree of freedom or parameter of the system is represented as an axis of a multidimensional space; a one-dimensional system is called a phase line, while a two-dimensional system is called a phase plane. For every possible state of the system or allowed combination of values of the system's parameters, a point is included in the multidimensional space. The system's evolving state over time traces a path (a phase-space trajectory for the system) through the high-dimensional space. The phase-space trajectory represents the set of states compatible with starting from one particular initial condition, located in the full phase space that represents the set of states compatible with starting from any initial condition. As a whole, the phase diagram represents all that the system can be, and its shape can easily elucidate qualities of the system that might not be obvious otherwise. A phase space may contain a great number of dimensions. For instance, a gas containing many molecules may require a separate dimension for each particle's x, y and z positions and momenta (6 dimensions for an idealized monatomic gas), and for more complex molecular systems additional dimensions are required to describe vibrational modes of the molecular bonds, as well as spin around 3 axes. Phase spaces are easier to use when analyzing the behavior of mechanical systems restricted to motion around and along various axes of rotation or translation – e.g. in robotics, like analyzing the range of motion of a robotic arm or determining the optimal path to achieve a particular position/momentum result.

Conjugate momenta
In classical mechanics, any choice of generalized coordinates qi for the position (i.e. coordinates on configuration space) defines conjugate generalized momenta pi, which together define co-ordinates on phase space. More abstractly, in classical mechanics phase space is the cotangent bundle of configuration space, and in this interpretation the procedure above expresses that a choice of local coordinates on configuration space induces a choice of natural local Darboux coordinates for the standard symplectic structure on a cotangent space.

Statistical ensembles in phase space
The motion of an ensemble of systems in this space is studied by classical statistical mechanics. The local density of points in such systems obeys Liouville's theorem, and so can be taken as constant. Within the context of a model system in classical mechanics, the phase-space coordinates of the system at any given time are composed of all of the system's dynamic variables. Because of this, it is possible to calculate the state of the system at any given time in the future or the past, through integration of Hamilton's or Lagrange's equations of motion.

In low dimensions
For simple systems, there may be as few as one or two degrees of freedom. One degree of freedom occurs when one has an autonomous ordinary differential equation in a single variable, $$dy/dt = f(y),$$ with the resulting one-dimensional system being called a phase line, and the qualitative behaviour of the system being immediately visible from the phase line. The simplest non-trivial examples are the exponential growth model/decay (one unstable/stable equilibrium) and the logistic growth model (two equilibria, one stable, one unstable).

The phase space of a two-dimensional system is called a phase plane, which occurs in classical mechanics for a single particle moving in one dimension, and where the two variables are position and velocity. In this case, a sketch of the phase portrait may give qualitative information about the dynamics of the system, such as the limit cycle of the Van der Pol oscillator shown in the diagram.

Here the horizontal axis gives the position, and vertical axis the velocity. As the system evolves, its state follows one of the lines (trajectories) on the phase diagram.

Phase plot
A plot of position and momentum variables as a function of time is sometimes called a phase plot or a phase diagram. However the latter expression, "phase diagram", is more usually reserved in the physical sciences for a diagram showing the various regions of stability of the thermodynamic phases of a chemical system, which consists of pressure, temperature, and composition.

Phase integral
In classical statistical mechanics (continuous energies) the concept of phase space provides a classical analog to the partition function (sum over states) known as the phase integral. Instead of summing the Boltzmann factor over discretely spaced energy states (defined by appropriate integer quantum numbers for each degree of freedom), one may integrate over continuous phase space. Such integration essentially consists of two parts: integration of the momentum component of all degrees of freedom (momentum space) and integration of the position component of all degrees of freedom (configuration space). Once the phase integral is known, it may be related to the classical partition function by multiplication of a normalization constant representing the number of quantum energy states per unit phase space. This normalization constant is simply the inverse of the Planck constant raised to a power equal to the number of degrees of freedom for the system.

Chaos theory
Classic examples of phase diagrams from chaos theory are:
 * the Lorenz attractor
 * population growth (i.e. logistic map)
 * parameter plane of complex quadratic polynomials with Mandelbrot set.

Quantum mechanics
In quantum mechanics, the coordinates p and q of phase space normally become Hermitian operators in a Hilbert space.

But they may alternatively retain their classical interpretation, provided functions of them compose in novel algebraic ways (through Groenewold's 1946 star product). This is consistent with the uncertainty principle of quantum mechanics. Every quantum mechanical observable corresponds to a unique function or distribution on phase space, and conversely, as specified by Hermann Weyl (1927) and supplemented by John von Neumann (1931); Eugene Wigner (1932); and, in a grand synthesis, by H. J. Groenewold (1946). With J. E. Moyal (1949), these completed the foundations of the phase-space formulation of quantum mechanics, a complete and logically autonomous reformulation of quantum mechanics. (Its modern abstractions include deformation quantization and geometric quantization.) Expectation values in phase-space quantization are obtained isomorphically to tracing operator observables with the density matrix in Hilbert space: they are obtained by phase-space integrals of observables, with the Wigner quasi-probability distribution effectively serving as a measure.

Thus, by expressing quantum mechanics in phase space (the same ambit as for classical mechanics), the Weyl map facilitates recognition of quantum mechanics as a deformation (generalization) of classical mechanics, with deformation parameter ħ/S, where S is the action of the relevant process. (Other familiar deformations in physics involve the deformation of classical Newtonian into relativistic mechanics, with deformation parameter v/c; or the deformation of Newtonian gravity into general relativity, with deformation parameter Schwarzschild radius/characteristic dimension.)

Classical expressions, observables, and operations (such as Poisson brackets) are modified by ħ-dependent quantum corrections, as the conventional commutative multiplication applying in classical mechanics is generalized to the noncommutative star-multiplication characterizing quantum mechanics and underlying its uncertainty principle.

Thermodynamics and statistical mechanics
In thermodynamics and statistical mechanics contexts, the term "phase space" has two meanings: for one, it is used in the same sense as in classical mechanics. If a thermodynamic system consists of N particles, then a point in the 6N-dimensional phase space describes the dynamic state of every particle in that system, as each particle is associated with 3 position variables and 3 momentum variables. In this sense, as long as the particles are distinguishable, a point in phase space is said to be a microstate of the system. (For indistinguishable particles a microstate consists of a set of N! points, corresponding to all possible exchanges of the N particles.) N is typically on the order of the Avogadro number, thus describing the system at a microscopic level is often impractical. This leads to the use of phase space in a different sense.

The phase space can also refer to the space that is parameterized by the macroscopic states of the system, such as pressure, temperature, etc. For instance, one may view the pressure–volume diagram or temperature–entropy diagram as describing part of this phase space. A point in this phase space is correspondingly called a macrostate. There may easily be more than one microstate with the same macrostate. For example, for a fixed temperature, the system could have many dynamic configurations at the microscopic level. When used in this sense, a phase is a region of phase space where the system in question is in, for example, the liquid phase, or solid phase, etc.

Since there are many more microstates than macrostates, the phase space in the first sense is usually a manifold of much larger dimensions than in the second sense. Clearly, many more parameters are required to register every detail of the system down to the molecular or atomic scale than to simply specify, say, the temperature or the pressure of the system.

Optics
Phase space is extensively used in nonimaging optics, the branch of optics devoted to illumination. It is also an important concept in Hamiltonian optics.

Medicine
In medicine and bioengineering, the phase space method is used to visualize multidimensional physiological responses.

title: Phase space