Foundations of Ergodic Theory

Self-contained introductory textbook suitable for a variety of one- or two-semester courses. Rich with examples, applications and exercises.

Marcelo Viana (Author), Krerley Oliveira (Author)

9781107126961, Cambridge University Press

Hardback, published 15 February 2016

548 pages, 35 b/w illus. 410 exercises
22.9 x 15.2 x 3.5 cm, 0.87 kg

'… 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

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.

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.

Subject Areas: Mathematical physics [PHU], Thermodynamics & heat [PHH], Applied mathematics [PBW], Mathematics [PB]