Ergodic Theory Independence and Dichotomies /

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 treat...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Kerr, David (Author), Li, Hanfeng (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
Edition:1st ed. 2016.
Series:Springer Monographs in Mathematics,
Subjects:
Dynamical systems.
Group theory.
Functional analysis.
Dynamical Systems.
Group Theory and Generalizations.
Functional Analysis.
Online Access:Texto Completo
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.

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