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  3. Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds
  • Cited by 58
Publisher:
Cambridge University Press
Online publication date:
May 2013
Print publication year:
1993
Online ISBN:
9780511752537
DOI:
https://doi.org/10.1017/CBO9780511752537
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory
Series:
London Mathematical Society Lecture Note Series (180)
Information

Book description

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.

Reviews

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

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