ebook9783319498478d4325

Description

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.