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Ergodic theory : independence and dichotomies / David Kerr, Hanfeng Li.

Kerr, David, author.; Li, Hanfeng, author.
2016
QA313
Available Online
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Title
Ergodic theory : independence and dichotomies / David Kerr, Hanfeng Li.
Author
Kerr, David, author.
ISBN
9783319498478 (electronic book)
3319498479 (electronic book)
9783319498454
Published
Cham, Switzerland : Springer, 2016.
Language
English
Description
1 online resource.
Call Number
QA313
Dewey Decimal Classification
515/.48
Summary
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.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed February 16, 2017).
Added Author
Li, Hanfeng, author.
Series
Springer monographs in mathematics.
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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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