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Ergodic Theory

Independence and Dichotomies

  • David Kerr
  • Hanfeng Li

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xxxiv
  2. David Kerr, Hanfeng Li
    Pages 1-18
  3. Weak Mixing and Compactness

    1. Front Matter
      Pages 19-19
    2. David Kerr, Hanfeng Li
      Pages 21-48
    3. David Kerr, Hanfeng Li
      Pages 49-72
    4. David Kerr, Hanfeng Li
      Pages 73-129
    5. David Kerr, Hanfeng Li
      Pages 131-146
    6. David Kerr, Hanfeng Li
      Pages 147-162
    7. David Kerr, Hanfeng Li
      Pages 163-178
    8. David Kerr, Hanfeng Li
      Pages 179-190
  4. Entropy

    1. Front Matter
      Pages 191-191
    2. David Kerr, Hanfeng Li
      Pages 193-229
    3. David Kerr, Hanfeng Li
      Pages 231-267
    4. David Kerr, Hanfeng Li
      Pages 269-282
    5. David Kerr, Hanfeng Li
      Pages 283-307
  5. Back Matter
    Pages 365-431

About this book

Introduction

This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment of the core concepts of weak mixing, compactness, entropy, and amenability. The more advanced material includes Popa's cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy.

The structure of the book is designed to be flexible enough to serve a variety of readers. The discussion of dynamics is developed from scratch assuming some rudimentary functional analysis, measure theory, and topology, and parts of the text can be used as an introductory course. Researchers in ergodic theory and related areas will also find the book valuable as a reference.

Keywords

Ergodic Theory Topological Dynamics Weak Mixing Entropy Entropy Independence Sofic Groups Homoclinicity Fuglede-Kadison Determinant Gaussian Hilbert Spaces Firstenberg-Zimmer Structure Theorem

Authors and affiliations

  • David Kerr
    • 1
  • Hanfeng Li
    • 2
  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA
  2. 2.Department of MathematicsSUNY BuffaloBuffaloUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-49847-8
  • Copyright Information Springer International Publishing AG 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-49845-4
  • Online ISBN 978-3-319-49847-8
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site
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