Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms
Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

Author: Robert Edward Bowen

Publisher: Springer Science & Business Media

Published: 2008-04-18

Total Pages: 84

ISBN-13: 3540776052

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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
Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

Author: Robert Edward Bowen

Publisher: Springer

Published: 2009-08-29

Total Pages: 80

ISBN-13: 9783540848875

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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."

Ergodic Theory
Ergodic Theory

Author: Cesar E. Silva

Publisher: Springer Nature

Published: 2023-07-31

Total Pages: 707

ISBN-13: 1071623885

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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
Equilibrium States in Ergodic Theory

Author: Gerhard Keller

Publisher: Cambridge University Press

Published: 1998-01-22

Total Pages: 196

ISBN-13: 9780521595346

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Based on a one semester course, this book provides a self contained introduction to the ergodic theory of equilibrium states.

Introduction to Smooth Ergodic Theory
Introduction to Smooth Ergodic Theory

Author: Luís Barreira

Publisher: American Mathematical Society

Published: 2023-04-28

Total Pages: 355

ISBN-13: 1470473070

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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
Dynamics, Ergodic Theory and Geometry

Author: Boris Hasselblatt

Publisher: Cambridge University Press

Published: 2007-09-24

Total Pages: 324

ISBN-13: 0521875412

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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.