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Ergodic Theory : Independence and Dichotomies
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| Abstract | 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.show more |
| 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.show more |
| Print Version | https://hdl.handle.net/2324/1001624473 |
| View fulltext | Springer Nature Mathematics and Statistics (R0) eBooks 2016 English/International: 2016 |
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| Created Date | 2023.09.29 |
| Modified Date | 2024.01.30 |