Foundations of Ergodic Theory
Foundations of Ergodic Theory
Krerley Oliveira, Universidade Federal de Alagoas, Brazil
Rich with examples and applications, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. The authors' clear and fluent exposition helps the reader to grasp quickly the most important ideas of the theory, and their use of concrete examples illustrates these ideas and puts the results into perspective. The book requires few prerequisites, with background material supplied in the appendix. The first four chapters cover elementary material suitable for undergraduate students – invariance, recurrence and ergodicity – as well as some of the main examples. The authors then gradually build up to more sophisticated topics, including correlations, equivalent systems, entropy, the variational principle and thermodynamical formalism. The 400 exercises increase in difficulty through the text and test the reader's understanding of the whole theory. Hints and solutions are provided at the end of the book.
- The authors' friendly explanations and use of examples make complex concepts easy to follow
- Self-contained so it can easily be adapted to a graduate or undergraduate course
- Contains more than 400 exercises, many with hints and solutions
Reviews & endorsements
'The book provides the student or researcher with an excellent reference and/or base from which to move into current research in ergodic theory. This book would make an excellent text for a graduate course on ergodic theory.' Douglas P. Dokken, Mathematical Reviews
'… Viana and Oliveira have written yet another excellent textbook! It may be fruitfully used to guide a graduate course in dynamical systems, or a topics seminar at either advanced undergraduate or early graduate levels. The book is designed so that the instructor may cull a variety of courses from its contents. The authors deserve special kudos for their collection of over 400 exercises, many with hints and solutions at the end of the book. As a further bonus, if only to pique the reader's interest, a number of recent research results and open problems are sprinkled throughout the book.' Tushar Das, MAA Reivews
Product details
No date availableAdobe eBook Reader
9781316447147
0 pages
0kg
35 b/w illus. 410 exercises
Table of Contents
- Preface
- 1. Recurrence
- 2. Existence of invariant measures
- 3. Ergodic theorems
- 4. Ergodicity
- 5. Ergodic decomposition
- 6. Unique ergodicity
- 7. Correlations
- 8. Equivalent systems
- 9. Entropy
- 10. Variational principle
- 11. Expanding maps
- 12. Thermodynamical formalism
- Appendix. Topics of measure theory, topology and analysis
- Hints or solutions for selected exercises
- References
- Index.
