Ergodic Theory

Beschreibung

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.
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.
Provides an introduction to the ergodic theory and topological dynamics of actions of general countable groups Covers several topics of current research interest, including Popa's cocycle superrigidity, sofic entropy, and algebraic actions Contains a consolidated account of amenability and its ramifications for dynamics, including a systematic exposition of the entropy theory for actions of amenable groups Includes supplementary material: sn.pub/extras

Autor*in

David Kerr

Themen in »Ergodic Theory«

Ergodic Theory Topological Dynamics Weak Mixing Entropy Entropy Independence Sofic Groups Homoclinicity Fuglede-Kadison Determinant Gaussian Hilbert Spaces Firstenberg-Zimmer Structure Theorem

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