エルゴード理論<br>Ergodic Theory〈1st ed. 2016〉 : Independence and Dichotomies

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紙書籍版価格 ¥18,455
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エルゴード理論
Ergodic Theory〈1st ed. 2016〉 : Independence and Dichotomies

  • 著者名:Kerr, David/Li, Hanfeng
  • 価格 ¥12,828 (本体¥11,878)
  • Springer(2017/02/09発売)
  • ポイント 118pt (実際に付与されるポイントはお支払い画面でご確認下さい)

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Description

This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups.&nbsp;It is organized around the theme of probabilistic and combinatorial independence,&nbsp;and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment&nbsp;of the core concepts of weak mixing, compactness, entropy, and amenability.&nbsp;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.&nbsp;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.&nbsp;Researchers in ergodic theory and related areas will also find the book valuable as a reference.

Table of Contents

Preface.- Introduction.- General Framework and Notational Conventions.- Part 1 Weak Mixing Comactness.- Basic Concepts in Ergodic Theory.- Structure Theory for P.M.P. Actions.- Amenability.- Property (T).- Orbit Equivalence Beyond Amenability.- Topological Dynamics.- Tameness and Independence.- Part 2 Entropy.- Entropy for Actions of Amenable Groups.- Entropy for Actions of Sofic Groups.- The f-invariant.- Entropy and Independence.- Algebraic Actions: Expansiveness, Homoclinicity, and Entropy.- Algebraic Actions: Entropy and the Fuglede-Kadison Determinant.- Appendix A. Polish Spaces and Standard Borel Spaces.- Appendix B. Positive Definite Functions and Weak Containment.- Appendix C. Hilbert Modules.- Appendix D. Weakly Almost Periodic Functions.- Appendix E. Gaussian Actions.