Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

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Publisher : Springer Science & Business Media
ISBN 13 : 3540776052
Total Pages : 84 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms by : Robert Edward Bowen

Download or read book Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms written by Robert Edward Bowen and published by Springer Science & Business Media. This book was released on 2008-04-18 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: For this printing of R. Bowen's book, J.-R. Chazottes has retyped it in TeX for easier reading, thereby correcting typos and bibliographic details. From the Preface by D. Ruelle: "Rufus Bowen has left us a masterpiece of mathematical exposition... Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic. More than thirty years later, many new results have been proved in this area, but the volume is as useful as ever because it remains the best introduction to the basics of the ergodic theory of hyperbolic systems."

Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

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Publisher : Springer
ISBN 13 : 9783540848875
Total Pages : 80 pages
Book Rating : 4.8/5 (488 download)

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Book Synopsis Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms by : Robert Edward Bowen

Download or read book Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms written by Robert Edward Bowen and published by Springer. This book was released on 2009-08-29 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: For this printing of R. Bowen's book, J.-R. Chazottes has retyped it in TeX for easier reading, thereby correcting typos and bibliographic details. From the Preface by D. Ruelle: "Rufus Bowen has left us a masterpiece of mathematical exposition... Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic. More than thirty years later, many new results have been proved in this area, but the volume is as useful as ever because it remains the best introduction to the basics of the ergodic theory of hyperbolic systems."

Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (77 download)

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Book Synopsis Equilibrium states and the ergodic theory of Anosov diffeomorphisms by : Rufus Bowen

Download or read book Equilibrium states and the ergodic theory of Anosov diffeomorphisms written by Rufus Bowen and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

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Publisher :
ISBN 13 : 9783662192702
Total Pages : 120 pages
Book Rating : 4.1/5 (927 download)

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Book Synopsis Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms by : R. Bowen

Download or read book Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms written by R. Bowen and published by . This book was released on 2014-01-15 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ergodic Theory

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Publisher : Springer Nature
ISBN 13 : 1071623885
Total Pages : 707 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Ergodic Theory by : Cesar E. Silva

Download or read book Ergodic Theory written by Cesar E. Silva and published by Springer Nature. This book was released on 2023-07-31 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras

Equilibrium States in Ergodic Theory

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Publisher : Cambridge University Press
ISBN 13 : 9780521595346
Total Pages : 196 pages
Book Rating : 4.5/5 (953 download)

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Book Synopsis Equilibrium States in Ergodic Theory by : Gerhard Keller

Download or read book Equilibrium States in Ergodic Theory written by Gerhard Keller and published by Cambridge University Press. This book was released on 1998-01-22 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a one semester course, this book provides a self contained introduction to the ergodic theory of equilibrium states.

Equilibrium States and the Ergodic Theory of Ansor Diffeomorphisms

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Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (52 download)

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Book Synopsis Equilibrium States and the Ergodic Theory of Ansor Diffeomorphisms by : Rufus Bowen

Download or read book Equilibrium States and the Ergodic Theory of Ansor Diffeomorphisms written by Rufus Bowen and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ergodic Theory of Equivariant Diffeomorphisms: Markov Partitions and Stable Ergodicity

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Publisher : American Mathematical Soc.
ISBN 13 : 0821835998
Total Pages : 113 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Ergodic Theory of Equivariant Diffeomorphisms: Markov Partitions and Stable Ergodicity by : Mike Field

Download or read book Ergodic Theory of Equivariant Diffeomorphisms: Markov Partitions and Stable Ergodicity written by Mike Field and published by American Mathematical Soc.. This book was released on 2004 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the assumption that the $\Gamma$-orbits all have dimension equal to that of $\Gamma$, this title shows that there is a naturally defined $F$- and $\Gamma$-invariant measure $\nu$ of maximal entropy on $\Lambda$ (it is not assumed that the action of $\Gamma$ is free).

Introduction to Smooth Ergodic Theory

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Publisher : American Mathematical Society
ISBN 13 : 1470473070
Total Pages : 355 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Introduction to Smooth Ergodic Theory by : Luís Barreira

Download or read book Introduction to Smooth Ergodic Theory written by Luís Barreira and published by American Mathematical Society. This book was released on 2023-04-28 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential equations, the concept of nonuniform hyperbolicity, stable manifold theory (with emphasis on absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. A detailed description of all the basic examples of conservative systems with nonzero Lyapunov exponents, including the geodesic flows on compact surfaces of nonpositive curvature, is also presented. There are more than 80 exercises. The book is aimed at graduate students specializing in dynamical systems and ergodic theory as well as anyone who wishes to get a working knowledge of smooth ergodic theory and to learn how to use its tools. It can also be used as a source for special topics courses on nonuniform hyperbolicity. The only prerequisite for using this book is a basic knowledge of real analysis, measure theory, differential equations, and topology, although the necessary background definitions and results are provided. In this second edition, the authors improved the exposition and added more exercises to make the book even more student-oriented. They also added new material to bring the book more in line with the current research in dynamical systems.

Dynamics, Ergodic Theory and Geometry

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Publisher : Cambridge University Press
ISBN 13 : 0521875412
Total Pages : 324 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Dynamics, Ergodic Theory and Geometry by : Boris Hasselblatt

Download or read book Dynamics, Ergodic Theory and Geometry written by Boris Hasselblatt and published by Cambridge University Press. This book was released on 2007-09-24 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the subjects from the Clay Mathematics Institute/Mathematical Sciences Research Institute Workshop titled 'Recent Progress in Dynamics' in September and October 2004, this volume contains surveys and research articles by leading experts in several areas of dynamical systems that have experienced substantial progress. One of the major surveys is on symplectic geometry, which is closely related to classical mechanics and an exciting addition to modern geometry. The survey on local rigidity of group actions gives a broad and up-to-date account of another flourishing subject. Other papers cover hyperbolic, parabolic, and symbolic dynamics as well as ergodic theory. Students and researchers in dynamical systems, geometry, and related areas will find this book fascinating. The book also includes a fifty-page commented problem list that takes the reader beyond the areas covered by the surveys, to inspire and guide further research.

Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110702681
Total Pages : 458 pages
Book Rating : 4.1/5 (17 download)

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Book Synopsis Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps by : Mariusz Urbański

Download or read book Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps written by Mariusz Urbański and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-11-22 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains a detailed treatment of thermodynamic formalism on general compact metrizable spaces. Topological pressure, topological entropy, variational principle, and equilibrium states are presented in detail. Abstract ergodic theory is also given a significant attention. Ergodic theorems, ergodicity, and Kolmogorov-Sinai metric entropy are fully explored. Furthermore, the book gives the reader an opportunity to find rigorous presentation of thermodynamic formalism for distance expanding maps and, in particular, subshifts of finite type over a finite alphabet. It also provides a fairly complete treatment of subshifts of finite type over a countable alphabet. Transfer operators, Gibbs states and equilibrium states are, in this context, introduced and dealt with. Their relations are explored. All of this is applied to fractal geometry centered around various versions of Bowen’s formula in the context of expanding conformal repellors, limit sets of conformal iterated function systems and conformal graph directed Markov systems. A unique introduction to iteration of rational functions is given with emphasize on various phenomena caused by rationally indifferent periodic points. Also, a fairly full account of the classicaltheory of Shub’s expanding endomorphisms is given; it does not have a book presentation in English language mathematical literature.

Smooth Ergodic Theory and Its Applications

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Publisher : American Mathematical Soc.
ISBN 13 : 0821826824
Total Pages : 895 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Smooth Ergodic Theory and Its Applications by : A. B. Katok

Download or read book Smooth Ergodic Theory and Its Applications written by A. B. Katok and published by American Mathematical Soc.. This book was released on 2001 with total page 895 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past decade, there have been several major new developments in smooth ergodic theory, which have attracted substantial interest to the field from mathematicians as well as scientists using dynamics in their work. In spite of the impressive literature, it has been extremely difficult for a student-or even an established mathematician who is not an expert in the area-to acquire a working knowledge of smooth ergodic theory and to learn how to use its tools. Accordingly, the AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications (Seattle, WA) had a strong educational component, including ten mini-courses on various aspects of the topic that were presented by leading experts in the field. This volume presents the proceedings of that conference. Smooth ergodic theory studies the statistical properties of differentiable dynamical systems, whose origin traces back to the seminal works of Poincare and later, many great mathematicians who made contributions to the development of the theory. The main topic of this volume, smooth ergodic theory, especially the theory of nonuniformly hyperbolic systems, provides the principle paradigm for the rigorous study of complicated or chaotic behavior in deterministic systems. This paradigm asserts that if a non-linear dynamical system exhibits sufficiently pronounced exponential behavior, then global properties of the system can be deduced from studying the linearized system. One can then obtain detailed information on topological properties (such as the growth of periodic orbits, topological entropy, and dimension of invariant sets including attractors), as well as statistical properties (such as the existence of invariant measures, asymptotic behavior of typical orbits, ergodicity, mixing, decay of corre This volume serves a two-fold purpose: first, it gives a useful gateway to smooth ergodic theory for students and nonspecialists, and second, it provides a state-of-the-art report on important current aspects of the subject. The book is divided into three parts: lecture notes consisting of three long expositions with proofs aimed to serve as a comprehensive and self-contained introduction to a particular area of smooth ergodic theory; thematic sections based on mini-courses or surveys held at the conference; and original contributions presented at the meeting or closely related to the topics that were discussed there.

Ergodic Theory and Dynamical Systems

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Publisher : Walter de Gruyter
ISBN 13 : 3110298201
Total Pages : 288 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Ergodic Theory and Dynamical Systems by : Idris Assani

Download or read book Ergodic Theory and Dynamical Systems written by Idris Assani and published by Walter de Gruyter. This book was released on 2013-12-12 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the proceedings of the workshop on recent developments in ergodic theory and dynamical systems on March 2011 and March 2012 at the University of North Carolina at Chapel Hill. The articles in this volume cover several aspects of vibrant research in ergodic theory and dynamical systems. It contains contributions to Teichmuller dynamics, interval exchange transformations, continued fractions, return times averages, Furstenberg Fractals, fractal geometry of non-uniformly hyperbolic horseshoes, convergence along the sequence of squares, adic and horocycle flows, and topological flows. These contributions illustrate the connections between ergodic theory and dynamical systems, number theory, harmonic analysis, probability, and algebra. Two surveys are included which give a nice introduction for interested young or senior researcher to some active research areas. Overall this volume provides a very useful blend of techniques and methods as well as directions of research on general convergence phenomena in ergodic theory and dynamical systems.

Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

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Publisher : Springer Science & Business Media
ISBN 13 : 3642565891
Total Pages : 816 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems by : Bernold Fiedler

Download or read book Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems written by Bernold Fiedler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.

Foundations of Ergodic Theory

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Publisher : Cambridge University Press
ISBN 13 : 1316445429
Total Pages : 547 pages
Book Rating : 4.3/5 (164 download)

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Book Synopsis Foundations of Ergodic Theory by : Marcelo Viana

Download or read book Foundations of Ergodic Theory written by Marcelo Viana and published by Cambridge University Press. This book was released on 2016-02-15 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rich with examples and applications, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. The authors' clear and fluent exposition helps the reader to grasp quickly the most important ideas of the theory, and their use of concrete examples illustrates these ideas and puts the results into perspective. The book requires few prerequisites, with background material supplied in the appendix. The first four chapters cover elementary material suitable for undergraduate students – invariance, recurrence and ergodicity – as well as some of the main examples. The authors then gradually build up to more sophisticated topics, including correlations, equivalent systems, entropy, the variational principle and thermodynamical formalism. The 400 exercises increase in difficulty through the text and test the reader's understanding of the whole theory. Hints and solutions are provided at the end of the book.

Dynamical Systems, Ergodic Theory and Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 9783540663164
Total Pages : 476 pages
Book Rating : 4.6/5 (631 download)

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Book Synopsis Dynamical Systems, Ergodic Theory and Applications by : L.A. Bunimovich

Download or read book Dynamical Systems, Ergodic Theory and Applications written by L.A. Bunimovich and published by Springer Science & Business Media. This book was released on 2000-04-05 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.

Ergodic Theory on Compact Spaces

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Publisher : Springer
ISBN 13 : 3540382631
Total Pages : 367 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Ergodic Theory on Compact Spaces by : M. Denker

Download or read book Ergodic Theory on Compact Spaces written by M. Denker and published by Springer. This book was released on 2006-11-14 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: