Foundations of Ergodic Theory

ISBN-13: 9781107126961 / Angielski / Twarda / 2016 / 548 str.

Marcelo Viana; Krerley Oliveira

Opis

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

Recenzje

'… 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

Spis treści

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.