Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds

These lecture notes provide a unique introduction to Pesin theory and its applications.

Mark Pollicott (Author)

9780521435932, Cambridge University Press

Paperback, published 4 February 1993

172 pages, 35 b/w illus.
22.7 x 15.1 x 1.1 cm, 0.29 kg

"...contains numerous simple examples which help the uninitiated reader to get a good idea of the relevance of the theorems..." Nicolai Haydn, Mathematical Reviews

Pesin theory consists of the study of the theory of non-uniformly hyperbolic diffeomorphisms. The aim of this book is to provide the reader with a straightforward account of this theory, following the approaches of Katok and Newhouse. The notes are divided into two parts. The first develops the basic theory, starting with general ergodic theory and introducing Liapunov exponents. Part Two deals with the applications of Pesin theory and contains an account of the existence (and distribution) of periodic points. It closes with a look at stable manifolds, and gives some results on absolute continuity. These lecture notes provide a unique introduction to Pesin theory and its applications. The author assumes that the reader has only a good background of undergraduate analysis and nothing further, so making the book accessible to complete newcomers to the field.

1. Invariant measures and some ergodic theory
2. Ergodic theory for manifolds and Liapunov exponents
3. Entropy
4. The Pesin set
5. Closing lemmas and periodic points
6. Structure of 'chaotic' diffeomorphisms
7. Stable manifolds and more measure theory
Appendix.

Subject Areas: Calculus & mathematical analysis [PBK]