Advertisement

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Ergodic Theory

    1. Front Matter
      Pages 1-1
    2. Yves Coudène
      Pages 3-14
    3. Yves Coudène
      Pages 15-24
    4. Yves Coudène
      Pages 25-33
    5. Yves Coudène
      Pages 35-46
  3. Dynamical Systems

    1. Front Matter
      Pages 47-47
    2. Yves Coudène
      Pages 49-57
    3. Yves Coudène
      Pages 59-67
    4. Yves Coudène
      Pages 69-78
    5. Yves Coudène
      Pages 79-88
    6. Yves Coudène
      Pages 89-98
  4. Entropy Theory

    1. Front Matter
      Pages 99-99
    2. Yves Coudène
      Pages 101-112
    3. Yves Coudène
      Pages 113-121
    4. Yves Coudène
      Pages 123-132
  5. Ergodic Decomposition

    1. Front Matter
      Pages 133-133
    2. Yves Coudène
      Pages 135-144
    3. Yves Coudène
      Pages 145-154
    4. Yves Coudène
      Pages 155-163
  6. Appendices

    1. Front Matter
      Pages 165-165
    2. Yves Coudène
      Pages 167-170
    3. Yves Coudène
      Pages 171-174
    4. Yves Coudène
      Pages 175-180
  7. Back Matter
    Pages 181-190

About this book

Introduction

This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics.

This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors.

Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of comments for the more advanced reader.

Keywords

Ergodic theory Dynamical systems Hyperbolic dynamics Chaotic attractors Entropy

Authors and affiliations

  • Yves Coudène
    • 1
  1. 1.Département de mathématiquesUniversité de Bretagne Occidentale Brest CEDEX 3France

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-7287-1
  • Copyright Information Springer-Verlag London 2016
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-7285-7
  • Online ISBN 978-1-4471-7287-1
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
Industry Sectors
Aerospace