Entropy in Dynamical Systems [Hardcover]

A comprehensive course on entropy in dynamical systems ideal for graduate students learning the subject from scratch.Students learning the subject from scratch will value this comprehensive text, which presents three major types of dynamics, from the basics to some of the latest results: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. It will also be a valuable reference for experienced researchers.Students learning the subject from scratch will value this comprehensive text, which presents three major types of dynamics, from the basics to some of the latest results: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. It will also be a valuable reference for experienced researchers.This comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the ShannonMcMillanBreiman Theorem, the OrnsteinWeiss Return Time Theorem, the Krieger Generator Theorem and, among the newest developments, the ergodic law of series. In Part II, after an expanded exposition of classical topological entropy, the book addresses Symbolic Extension Entropy. It offers deep insight into the theory of entropy structure and explains the role of zero-dimensional dynamics as a bridge between measurable and topological dynamics. Part III explains how both measure-theoretic and topological entropy can be extended to operators on relevant function spaces. Intuitive explanations, examples, exercises and open problems make this an ideal text for a graduate course on entropy theory. More experienced researchers can also find inspiration for further research.Introduction; Part I. Entropy in Ergodic Theory: 1. Shannon information and entropy; 2. Dynamical entropy of a process; 3. Entropy theorems in processes; 4. KolmogorovSinai entropy; 5. The ergodic law ofl£{