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...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2016, 2016
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| Edition: | 1st ed. 2016 |
| Series: | Springer Monographs in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
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