Volume: 95; 2000; 113 pp; Softcover
MSC: Primary 22; 28; 60;
Print ISBN: 978-0-8218-0414-8
Product Code: CBMS/95
List Price: $27.00
Individual Price: $21.60
Electronic ISBN: 978-1-4704-2455-8
Product Code: CBMS/95.E
List Price: $25.00
Individual Price: $20.00
Single Orbit Dynamics
Share this pageBenjamin Weiss
A co-publication of the AMS and CBMS
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 Shannon-Breiman-McMillan 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 & Endorsements
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
Table of Contents
Single Orbit Dynamics
- Cover Cover11 free
- Title v6 free
- Copyright vi7 free
- Contents vii8 free
- Preface ix10 free
- Chapter 1. What is Single Orbit Dynamics 112 free
- Chapter 2. Topological Dynamics 1223
- Chapter 3. Invariant Measures, Ergodicity and Unique Ergodicity 2334
- Chapter 4. Ergodic and Uniquely Ergodic Orbits 3950
- Chapter 5. Translation Invariant Graphs and Recurrence 4859
- Chapter 6. Patterns in Large Sets 5869
- Chapter 7. Entropy and Disjointness 6778
- Chapter 8. What is Randomness 8394
- Chapter 9. Recurrence Rates and Entropy 95106
- Chapter 10. Universal Schemes 104115
- Back Cover Back Cover1127