Dynamical Systems II

Ergodic Theory with Applications to Dynamical Systems and Statistical Mechanics

  • Ya. G. Sinai

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

Table of contents

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

    1. Front Matter
      Pages 1-2
    2. I. P. Cornfeld, Ya. G. Sinai
      Pages 28-36
    3. I. P. Cornfeld, Ya. G. Sinai
      Pages 36-58
    4. A. M. Vershik
      Pages 77-92
  3. Ergodic Theory of Smooth Dynamical Systems

  4. Dynamical Systems of Statistical Mechanics and Kinetic Equations

    1. Front Matter
      Pages 207-208
    2. R. L. Dobrushin, Ya. G. Sinai, Yu. M. Sukhov
      Pages 208-254
  5. Back Matter
    Pages 279-284

About this book

Introduction

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.

Keywords

dynamical systems ergodic theory ergodicity mechanics mixing statistical mechanics

Editors and affiliations

  • Ya. G. Sinai
    • 1
  1. 1.Landau Institute of Theoretical PhysicsMoscowUSSR

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-06788-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-06790-1
  • Online ISBN 978-3-662-06788-8
  • Series Print ISSN 0938-0396
  • About this book