CBMS Regional Conference Series in Mathematics 2000; 113 pp; softcover Number: 95 ISBN10: 0821804146 ISBN13: 9780821804148 List Price: US$25 Member Price: US$20 All Individuals: US$20 Order Code: CBMS/95
 This book presents the expanded notes from ten lectures given by the author at the NSF/CBMS conference held at California State University (Bakersfield). The author describes what he calls single orbit dynamics, which is an approach to the analysis of dynamical systems via the study of single orbits, rather than the study of a system as a whole. He presents single orbit interpretations of several areas of topological dynamics and ergodic theory and some new applications of dynamics to graph theory. In the concluding lectures, single orbit approaches to generalizations of the ShannonBreimanMcMillan theorem and related problems of compression and universal coding are presented. Complete proofs and illuminating discussions are included and references for further study are given. Some of the material appears here for the first time in print. Readership Graduate students and research mathematicians interested in dynamical systems. Reviews "These notes give a unique tour through modern dynamical systems in the broadest sense. The perspective is unique, and the exposition is clear enough for the notes to be of value to graduate students in ergodic theory and dynamical systems or probability, as well as being essential reading for experts."  Mathematical Reviews Table of Contents  What is single orbit dynamics
 Topological dynamics
 Invariant measures, ergodicity and unique ergodicity
 Ergodic and uniquely ergodic orbits
 Translation invariant graphs and recurrence
 Patterns in large sets
 Entropy and disjointness
 What is randomness?
 Recurrence rates and entropy
 Universal schemes
