Description
Book SynopsisOffers an introduction to modern ergodic theory. It emphasizes a new approach that relies on the technique of joining two (or more) dynamical systems. This approach has proved to be fruitful in many recent works. This is the first time that the entire theory has been presented from a joining perspective.
Table of Contents
- Introduction
- General group actions
- Topological dynamics
- Dynamical systems on Lebesgue spaces
- Ergodicity and mixing properties
- Invariant measures on topological systems
- Spectral theory
- Joinings
- Some applications of joinings
- Quasifactors Isometric and weakly mixing extensions
- The Furstenberg-Zimmer structure theorem
- Host's theorem
- Simple systems and their self-joinings
- Kazhdan's property and the geometry of $M_{\Gamma}(\mathbf{X})$
- Entropy theory for $\mathbb{Z}$-systems
- Entropy
- Symbolic representations
- Constructions
- The relation between measure and topological entropy
- The Pinsker algebra, CPE and zero entropy systems
- Entropy pairs
- Krieger's and Ornstein's theorems
- Prerequisite background and theorems
- Bibliography
- Index of symbols
- Index of terms
