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Basic ergodic theory

  • Book
  • © 2013

Overview

Authors:
  1. M. G. Nadkarni

    1. University of Mumbai, India

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Part of the book series: Texts and Readings in Mathematics (TRM, volume 6)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xiii
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  2. The Poincaré Recurrence Lemma

    • M. G. Nadkarni
    Pages 1-12

  3. Ergodic Theorems of Birkhoff and von Neumann

    • M. G. Nadkarni
    Pages 13-33

  4. Ergodicity

    • M. G. Nadkarni
    Pages 34-43

  5. Mixing Conditions and Their Characterisations

    • M. G. Nadkarni
    Pages 44-52

  6. Bernoulli Shift and Related Concepts

    • M. G. Nadkarni
    Pages 53-62

  7. Discrete Spectrum Theorem

    • M. G. Nadkarni
    Pages 63-67

  8. Induced Automorphisms and Related Concepts

    • M. G. Nadkarni
    Pages 68-82

  9. Borel Automorphisms are Polish Homeomorphisms

    • M. G. Nadkarni
    Pages 83-86

  10. The Glimm-Effros Theorem

    • M. G. Nadkarni
    Pages 87-97

  11. E. Hopf’s Theorem

    • M. G. Nadkarni
    Pages 98-119

  12. H. Dye’s Theorem

    • M. G. Nadkarni
    Pages 120-132

  13. Flows and Their Representations

    • M. G. Nadkarni
    Pages 133-148

  14. Additional Topics

    • M. G. Nadkarni
    Pages 149-175

  15. Back Matter

    Pages 177-190
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About this book

This is an introductory book on Ergodic Theory. The presentation has a slow pace and the book can be read by any person with a background in basic measure theory and metric topology. A new feature of the book is that the basic topics of Ergodic Theory such as the Poincare recurrence lemma, induced automorphisms and Kakutani towers, compressibility and E. Hopf's theorem, the theorem of Ambrose on representation of flows are treated at the descriptive set-theoretic level before their measure-theoretic or topological versions are presented. In addition, topics around the Glimm-Effros theorem are discussed. In the third edition a chapter entitled 'Additional Topics' has been added. It gives Liouville's Theorem on the existence of invariant measure, entropy theory leading up to Kolmogorov-Sinai Theorem, and the topological dynamics proof of van der Waerden's theorem on arithmetical progressions.

Authors and Affiliations

  • University of Mumbai, India

    M. G. Nadkarni

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