Chapter 2 Entropy, isomorphism and equivalence in ergodic theory

Abstract

Publisher Summary This chapter discusses the core of abstract ergodic theory: the Ornstein Isomorphism theory and the theory of Kakutani equivalence. The objects with which these theories are concerned are abundantly supplied by many sources from diversified origins. Criteria described in the chapter allow establishing those properties in many cases of interest, including absolutely continuous, Sinai–Ruelle–Bowen (SRB) and Gibbs measures for systems with hyperbolic behavior. The Ornstein isomorphism theory has been mostly developed in the early seventies and the theory of Kakutani equivalence from mid-seventies through early eighties. While plenty of interesting and important work in both areas appeared later, the basic form of the two theories has not changed.