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Dynamical Systems II

Ergodic Theory with Applications to Dynamical Systems and Statistical Mechanics

  • Book
  • © 1989

Overview

Editors:
  1. Ya. G. Sinai

    1. Landau Institute of Theoretical Physics, Moscow, USSR

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Part of the book series: Encyclopaedia of Mathematical Sciences (EMS, volume 2)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-IX
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  2. General Ergodic Theory of Groups of Measure Preserving Transformations

    1. Front Matter

      Pages 1-2
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    2. Basic Notions of Ergodic Theory and Examples of Dynamical Systems

      • I. P. Cornfeld, Ya. G. Sinai
      Pages 2-27

    3. Spectral Theory of Dynamical Systems

      • I. P. Cornfeld, Ya. G. Sinai
      Pages 28-36

    4. Entropy Theory of Dynamical Systems

      • I. P. Cornfeld, Ya. G. Sinai
      Pages 36-58

    5. Periodic Approximations and Their Applications. Ergodic Theorems, Spectral and Entropy Theory for the General Group Actions

      • I. P. Cornfeld, A. M. Vershik
      Pages 59-77

    6. Trajectory Theory

      • A. M. Vershik
      Pages 77-92

  3. Ergodic Theory of Smooth Dynamical Systems

    1. Front Matter

      Pages 99-101
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    2. Stochasticity of Smooth Dynamical Systems. The Elements of KAM-Theory

      • Ya. G. Sinai
      Pages 101-108

    3. General Theory of Smooth Hyperbolic Dynamical Systems

      • Ya. B. Pesin
      Pages 108-151

    4. Dynamical Systems of Hyperbolic Type with Singularities

      • L. A. Bunimovich
      Pages 151-178

    5. Ergodic Theory of One-Dimensional Mappings

      • M. V. Jakobson
      Pages 179-199

  4. Dynamical Systems of Statistical Mechanics and Kinetic Equations

    1. Front Matter

      Pages 207-208
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    2. Dynamical Systems of Statistical Mechanics

      • R. L. Dobrushin, Ya. G. Sinai, Yu. M. Sukhov
      Pages 208-254

    3. Existence and Uniqueness Theorems for the Boltzmann Equation

      • N. B. Maslova
      Pages 254-276

  5. Back Matter

    Pages 279-284
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Keywords

About this book

Following the concept of the EMS series this volume sets out to familiarize the reader to the fundamental ideas and results of modern ergodic theory and to its applications to dynamical systems and statistical mechanics. The exposition starts from the basic of the subject, introducing ergodicity, mixing and entropy. Then the ergodic theory of smooth dynamical systems is presented - hyperbolic theory, billiards, one-dimensional systems and the elements of KAM theory. Numerous examples are presented carefully along with the ideas underlying the most important results. The last part of the book deals with the dynamical systems of statistical mechanics, and in particular with various kinetic equations. This book is compulsory reading for all mathematicians working in this field, or wanting to learn about it.

Editors and Affiliations

  • Landau Institute of Theoretical Physics, Moscow, USSR

    Ya. G. Sinai

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