Ergodic Theory Independence and Dichotomies

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Synopsis

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.

Book details

Edition:
1st ed. 2016
Series:
Springer Monographs in Mathematics
Author:
David Kerr, Hanfeng Li
ISBN:
9783319498478
Related ISBNs:
9783319498454
Publisher:
Springer International Publishing
Pages:
N/A
Reading age:
Not specified
Includes images:
Yes
Date of addition:
2019-09-25
Usage restrictions:
Copyright
Copyright date:
2016
Copyright by:
Springer International Publishing, Cham 
Adult content:
No
Language:
English
Categories:
Mathematics and Statistics, Nonfiction