Published February 21, 2017
Hanfeng Li has co-authored a new book with David Kerr, entitled, Ergodic Theory: Independence and Dichotomies. The book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups.
The book 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.
Excerpts from back cover: 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.