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	Ergodic theory - Wikipedia, the free encyclopedia
		The ergodicity of the geodesic flow on manifolds of constant negative curvature was discovered by E.
		Ergodicity of geodesic flow in symmetric spaces was given by F.
		A simple criterion for the ergodicity of a homogeneous flow on a homogeneous space of a semisimple Lie group was given by C.
	en.wikipedia.org /wiki/Ergodic_theory (633 words)

	Ergodic literature - Wikipedia, the free encyclopedia
		Ergodic literature is literature that requires special effort to comprehend or read, perhaps due to a "non linear" structure.
		For example, ergodic literature may require following a very unconventional page layout in order to understand a novel, or in the case of ebooks, readers may need to constantly use hyperlinks to follow the narrative, or use menus to continue reading in a new location.
		Although it may be supposed that this kind of literature was born in the second half of the 20th century, at the same time as the first appearance of computers, critics of the ergodic literature have often mentioned the I Ching as the first example of genre.
	en.wikipedia.org /wiki/Ergodic_literature (293 words)

	Ergodic literature - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-22)
		Ergodic literature is literature that requires special effort to navigate.
		Ergodic texts demands on who was reading, to play an active role.
		Another good example of ergodic literature is Composition No.1, a novel on cards written by Marc Saporta in 1961.
	encyclopedia.worldsearch.com /ergodic_literature.htm (312 words)

	the cutscene is an essential part of a game’s rhetorical and intertextual address to the player, a dimension of ...
		The ergodic signifies the general principle of having to work with the materiality of a text, the need to participate in the construction of its material structure.
		As a discursive mode, the ergodic can be contrasted to narrative discourse, where the user is invited only to engage in the semantics of the text and does not have to worry about its material configuration.
		In the latter case, the ergodic effort is all about the configuration of the material discourse, revealing no other relation to the semantics of this discourse.
	www.uib.no /People/smkrk/docs/klevjerpaper.htm (4789 words)

	Ergodic theory - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-22)
		Another consequence of the ergodic theorem is that the average recurrence time of A is inversely proportional to the measure of A,
		Ergodic Theory and Harmonic Analysis : Proceedings of the 1993 Alexandria Conference (London Mathematical Society Lecture Note Series)
		Ergodic Theory and Topological Dynamics (Pure and applied mathematics, a series of monographs and textbooks)
	encyclopedia.worldsearch.com /ergodic_theory.htm (358 words)

	Ergodic theory group
		Ergodic hypothesis was first formulated for systems of particles, subject to known interactions and having known masses, evolving in a domain of the 3 dimensional space.
		Ergodic hypothesis is equivalent in stating that most of the trajectories are uniformly distributed on surfaces of constant energy of the phase space; moreover, asymptotically, it allows the replacement of time averages by spatial averages.
		Beyond the strict probabilistic framework, methods of ergodic theory are applied to problems of geometric or arithmetic nature or to models stemming from mathematical physics.
	www.math.univ-rennes1.fr /theoergo/index.html.en.html (406 words)

	Games Studies 0102: The myth of the ergodic videogame. By James Newman
		While they may contain interactive or ergodic elements, it is a mistake to consider that they present only one type of experience and foster only one type of engagement.
		Play sequences, from where the idea of the interactivity or ergodicity of videogames derives, are framed and punctuated by movie sequences, map screens, score or lap-time feedback screens and so on.
		While the concept of ergodicity, being grounded in a concrete definition, is immeasurably favourable, it is important to note that its application to videogames is by no means simple.
	www.gamestudies.org /0102/newman (4803 words)

	Johan Svedjedal : A Note on the Concept of "Hypertext"
		This would be an ergodic version of the work – a non-hyperwork masquerading as a hyperwork.
		Ergodic forms are works like Michael Joyce’s afternoon, used and read in their digital environments.
		In such ergodic and multisequential hyperworks, the links are written into the narrative, not imposed on it afterwards.
	www.hb.se /bhs/ith/3-99/js.htm (4689 words)

	Read This: Ergodic Theory of Numbers
		The ergodic theorem is then applied to, as stated in the preface, "obtain old and new results in an elegant and straightforward manner".
		The Ergodic Theorem, coupled with the natural extension machinery applied to the Gauss map, is used in chapter 5 to obtain arithmetical properties of the approximation coefficients for continued fraction expansions.
		Ergodicity and the Ergodic Theorem are used as tools to arrive at results of interest to the authors.
	www.maa.org /reviews/ergodicnt.html (3054 words)

	Ergodic theory (Site not responding. Last check: 2007-10-22)
		Ergodic theory the study of ergodic transformations grew of an attempt to prove the ergodic hypothesis of statistical physics.
		For an ergodic transformation time mean is equal to the space almost everywhere.
		This is the celebrated ergodic theorem in an abstract form due to David Birkhoff.
	www.freeglossary.com /Ergodicity (434 words)

	Ergodic Theory
		In simple terms Ergodic theory is the study of long term averages of dynamical systems.
		The kind of Ergodic Theory I do is concerned with measure preserving transformations (m.p.t.'s) of a Lebesgue space (i.e.
		Properties of transformations that are invariant under isomorphism include ergodicity, weak mixing, mixing, and entropy.
	www2.potsdam.edu /madorebf/ergodic.htm (481 words)

	Grand Text Auto » Clarifying Ergodic and Cybertext (Site not responding. Last check: 2007-10-22)
		This phenomenon I call ergodic, using a term appropriated from physics that derives from the Greek words ergon and hodos, meaning “work” and “path.” In ergodic literature, nontrivial effort is required to allow the reader to traverse the text.
		If ergodic literature is to make sense as a concept, there must also be nonergodic literature, where the effort to traverse the text is trivial, with no extranoematic responsibilities placed on the reader except (for example) eye movement and the periodic or arbitrary turning of pages.
		The ergodic work of art is one that in a material sense includes the rules for its own use, a work that has certain requirements built in that automatically distinguishes between successful and unsuccessful users.
	grandtextauto.gatech.edu /2005/08/12/clarifying-ergodic-and-cybertext (7946 words)

	Ergodic Theory and Geometric Rigidity and Number Theory
		The central scientific theme of this programme was the recent development of applications of ergodic theory to other areas of mathematics, in particular, the connections with geometry, group actions and rigidity, and number theory.
		Ergodic theory is an area of mathematics with all of its roots and development contained within the 20th century.
		Finally, Kaimanovich and Schmidt took the opportunity to continue their work on the ergodicity of horocycle foliations of certain non-negatively curved manifolds, by extending the types of covers of compact manifolds for which they can show the horocycle action is ergodic.
	www.newton.cam.ac.uk /reports/9900/ern.html (3103 words)

	INI Programme ERN (Site not responding. Last check: 2007-10-22)
		The central scientific theme of this programme is the recent development of applications of ergodic theory to other areas of mathematics.
		The potential of ergodic theory as a tool in number theory was revealed by Furstenberg's proof of Szemerdi's theorem on arithmetic progressions.
		Of equal importance is the role of ergodic theory in geometry and the rigidity of actions.
	www.newton.cam.ac.uk /programs/old_progs/ERN/ern.html (205 words)

	Boltzmann's Work in Statistical Physics
		Particularly notorious are the role of the ergodic hypothesis and the status of the so-called H-theorem.
		It seems that Boltzmann regarded the ergodic hypothesis as a special dynamical assumption that may or may not be true, depending on the nature of the system, and perhaps also on its initial state.
		It is indeed evident that if the ergodic hypothesis holds, a state will spend time in the various regions of phase space in proportion to their volume.
	setis.library.usyd.edu.au /stanford/entries/statphys-Boltzmann (12990 words)

	Education activities of karma (Site not responding. Last check: 2007-10-22)
		The roots of ergodic theory go back to Boltzmann's ergodic hypothesis concerning the equality of the time mean and the space mean of molecules in a gas, i.e., the long term time average along a single trajectory should equal the average over all trajectories.
		Nowadays, ergodic theory is known as the probabilistic (or measurable) study of the average behavior of ergodic systems, i.e., systems evolving in time that are in equilibrium and ergodic.
		The first major contribution in ergodic theory is the generalization of the strong law of large numbers to stationary and ergodic processes (seen as sequences of measurements on your system).
	www.math.uu.nl /people/dajani/eduM.html (392 words)

	Books on Ergodic Theory (Site not responding. Last check: 2007-10-22)
		The focus is on models of dynamical processes affected by white noise, which are described by partial differential equations such as the reaction-diffusion equations or Navier-Stokes equations.
		It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience.
		Ergodic Theory grew out of an important problem of statistical mechanics which was resolved by Birkhoff and von Neumann in the 1930s.
	books.bankhacker.com /Ergodic+Theory (684 words)

	Ergodic Theory at UEA (Site not responding. Last check: 2007-10-22)
		Ergodic theory is the study of statistical properties of deterministic dynamical systems.
		Research activity at UEA in ergodic theory is focused on higher dimensional Markov shifts (dynamical systems in which the acting group is a lattice) and connections between arithmetic and ergodic theory.
		`Ergodic Theory' by I.P. Cornfeld, S.V. Fomin and Ya.G. Sinai, Springer-Verlag (1981).
	www.mth.uea.ac.uk /~h720/research (534 words)

	Impact of the simulation algorithm, magnitude of ergodic fluc... (Site not responding. Last check: 2007-10-22)
		Goovaerts, P. Impact of the simulation algorithm, magnitude of ergodic fluctuations and number of realizations on the spaces of uncertainty of flow predictions.
		The impact of ergodic fluctuations and number of realizations on the extent of the space of uncertainty is also investigated.
		The attenuation of ergodic fluctuations through a rank-preserving transform of permeability values reduces substantially the extent of the space of uncertainty for sequential indicator simulation and p-field simulation, while improving the prediction of the response variable by the mean of the output distribution.
	www.ai-geostats.org /papers/_papers/0000001b.htm (404 words)

	Ordway Lectures 2004: Furstenberg, Hillel - math.umn.edu (Site not responding. Last check: 2007-10-22)
		We discuss briefly the historical background for Ergodic Theory and the notion of ergodic systems which form the building blocks for this theory.
		Ergodic systems can be classified by the degree of forgetfulness - or randomness - which they display.
		"Ergodic Geometry" enables one to isolate "geometrically meaningful" objects in the context of ergodic (rather than transitive) group actions,and the rudimentary study of these leads to a "completion" of the acting group.
	www.math.umn.edu /ordway/2004/furstenberg (321 words)

	Ergodic Theorems and Related Problems
		In the theory of stationary processes ergodicity is often identified with metric transitivity.
		In the theory of Markov processes, the word ergodic is applied to theorems of both the existence of transition probability limits and on the convergence of mean value ratios of these transition probabilities.
		In this book, an ergodic theorem refers to any statement about the existence of a mean value with respect to trajectories of a random process taken with respect to time.
	www.vsppub.com /books/mathe/bk-ErgTheRelPro.html (227 words)

	Preface: Discrete sample paths
		Of particular note in the discussion of process models is how ergodic theorists think of a stationary process, namely, as a measure-preserving transformation on a probability space, together with a partition of the space.
		The audiences included ergodic theorists, information theorists, and probabilists, as well as combinatorialists and people from engineering and other mathematics disciplines, ranging from undergraduate and graduate students through post-docs and junior faculty to senior professors and researchers.
		Many standard topics from ergodic theory are omitted or given only cursory treatment, in part because the book is already too long and in part because they are not close to the central focus of this book.
	www.math.utoledo.edu /~pshields/preface.html (1104 words)

	Introductory Lectures on Ergodic Theory, Geometry and Lie Groups 4
		Ergodic theory and the geometry of fractals I
		Ergodic theory and the geometry of fractals II Coffee
		Ergodic theory and the geometry of fractals III
	www.newton.cam.ac.uk /programmes/old_progs/ERN/ernw01p.html (227 words)

	Ergodic Theory Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-22)
		Looking For ergodic theory - Find ergodic theory and more at Lycos Search.
		Find ergodic theory - Your relevant result is a click away!
		The article on Anosov flows provides an example of ergodic flows on SL(2,R) and more generally on Riemann surfaces of negative curavture.
	www.greatartworks.com /encyclopedia/Ergodic_theory (803 words)

	ERGODIC (Site not responding. Last check: 2007-10-22)
		A collection of systems forms an ergodic ensemble if the modes of behavior found in any one system from time to time resemble its behavior at other temporal periods and if the behavior of any other system when chosen at random also is like the one system.
		Attribute of a behavior that involves only equilibrium states and whose transition probabilities either are unvarying or follow a definite cycle.
		In statistics, ergodicity is called stationarity and tested by comparing the transition probabilities or different parts of a longer sequence of events.
	pespmc1.vub.ac.be /ASC/ERGODIC.html (235 words)

	Ergodic Hypothesis
		Boltzmann tried to resolve the problem by means of "the Ergodic Hypothesis." The intuitive idea of this hypothesis may be informally explained this way.
		We have already seen that the assumption of equiprobability of all micro-states leads to the conclusion that the state of equilibrium is most probably realized in any gas, thereby supporting the second law of thermodynamics in a probabilistic way.
		And the H-Theorem should now be understood as saying that the time-average of the equilibrium state or those states which are close to the equilibrium is as large as being almost identical to one.
	www.bun.kyoto-u.ac.jp /~suchii/reduction7.html (320 words)

	Ergodic Boundary/Point Control of Stochastic Semilinear Systems (Site not responding. Last check: 2007-10-22)
		A controlled Markov process in a Hilbert space and an ergodic cost functional are given for a control problem that is solved where the process is a solution of a parameter-dependent semilinear stochastic differential equation and the control can occur only on the boundary or at discrete points in the domain.
		Some ergodic properties of the controlled Markov process are shown to be uniform in the control and the parameter.
		The existence of an optimal control is verified to solve the ergodic control problem.
	epubs.siam.org /sam-bin/dbq/article/30319 (187 words)

	Citations: The ergodic and entropy theorems revisited - Shields (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		We consider the interrelations of stationary and ergodic properties of processes that are stationary or ergodic with respect to block....
		P.C. Shields, "The Ergodic and Entropy Theorems Revisited," IEEE Trans.
		Shields, The ergodic and entropy theorems revisited, IEEE Trans.
	citeseer.ist.psu.edu /context/607065/0 (574 words)

	Research (Site not responding. Last check: 2007-10-22)
		Ergodic theory can be thought of as understanding the behaviour of typical orbits.
		If G is a cocompact group then the orbit G(x,y) is dense and the action is ergodic, as was shown by Hedlund (1936).
		Although not all such frame flows are ergodic, Brin, Gromov and Karcher showed in the 1980s that ergodicity holds for manifolds close to constant curvature (except in dimensions 7 and 8)
	www.ma.man.ac.uk /~mp/research.html (1119 words)

	Arkady Tempelman - 0792317173 - Gordon Inkeles Iris Schencke (Site not responding. Last check: 2007-10-22)
		Ergodic Theory and Its Connection With Harmonic Analysis Proceedings of the 1993 Alexandria Conference London Mathematical Society Lecture Note 2.
		Ergodic Theory and Differentiable Dynamics A Series of Modern Surveys in Mathematics Vol 8.
		Ergodic concepts in stellar dynamics proceeedings of an international workshop held at Geneva Observatory University of Geneva Switzerland 1 - 3 March 1993.
	www.howtowrite.net /137066ergodic_theorems_group_actions_informational_thermodynamical_aspects_mathematics_applications_78.html (190 words)

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