Ergodic Theory [Paperback]

This book presents the fundamentals of ergodic theory as well as selected advanced topics.The fundamentals of the ergodic theory of point transformations are presented along with several advanced topics of intense research in this well documented study of dynamical systems.The fundamentals of the ergodic theory of point transformations are presented along with several advanced topics of intense research in this well documented study of dynamical systems.The author presents the fundamentals of the ergodic theory of point transformations and several advanced topics of intense research. The study of dynamical systems forms a vast and rapidly developing field even when considering only activity whose methods derive mainly from measure theory and functional analysis. Each of the basic aspects of ergodic theory--examples, convergence theorems, recurrence properties, and entropy--receives a basic and a specialized treatment. The author's accessible style and the profusion of exercises, references, summaries, and historical remarks make this a useful book for graduate students or self study.Preface; 1. Introduction and preliminaries; 2. The fundamentals of ergodic theory; 3. More about almost everywhere convergence; 4. More about recurrence; 5. Entropy; 6. More about entropy; References; Index. For an introduction and general survey, Petersen's book is an excellent choice. Nathaniel Friedman, Mathematical Reviews