**Graduate Studies in Mathematics**

Volume: 148;
2013;
277 pp;
Hardcover

MSC: Primary 37;

Print ISBN: 978-0-8218-9853-6

Product Code: GSM/148

List Price: $65.00

Individual Member Price: $52.00

**Electronic ISBN: 978-1-4704-0972-2
Product Code: GSM/148.E**

List Price: $65.00

Individual Member Price: $52.00

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#### Supplemental Materials

# Introduction to Smooth Ergodic Theory

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*Luis Barreira; Yakov Pesin*

This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential equations, the concept of nonuniform hyperbolicity, stable manifold theory (with emphasis on the absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. The authors also present a detailed description of all basic examples of conservative systems with nonzero Lyapunov exponents, including the geodesic flows on compact surfaces of nonpositive curvature.

This book is a revised and considerably expanded version of the
previous book by the same authors *Lyapunov Exponents and Smooth
Ergodic Theory* (University Lecture Series, Vol. 23, AMS, 2002). It
is aimed at graduate students specializing in dynamical systems and
ergodic theory as well as anyone who wants to acquire a working
knowledge of smooth ergodic theory and to learn how to use its
tools. With more than 80 exercises, the book can be used as a primary
textbook for an advanced course in smooth ergodic theory. The book is
self-contained and only a basic knowledge of real analysis, measure
theory, differential equations, and topology is required and, even so,
the authors provide the reader with the necessary background
definitions and results.

#### Table of Contents

# Table of Contents

## Introduction to Smooth Ergodic Theory

- Cover Cover11 free
- Title page i2 free
- Contents iii4 free
- Preface vii8 free
- Part I. The core of the theory 112 free
- Examples of hyperbolic dynamical systems 314
- General theory of Lyapunov exponents 3344
- Lyapunov stability theory of nonautonomous equations 6172
- Elements of the nonuniform hyperbolicity theory 7788
- Cocycles over dynamical systems 99110
- The Multiplicative Ergodic Theorem 113124
- Local manifold theory 133144
- Absolute continuity of local manifolds 155166
- Ergodic properties of smooth hyperbolic measures 171182
- Geodesic flows on surfaces of nonpositive curvature 195206
- Part II. Selected advanced topics 213224
- Cone technics 215226
- Partially hyperbolic diffeomorphisms with nonzero exponents 223234
- More examples of dynamical systems with nonzero Lyapunov exponents 235246
- Anosov rigidity 247258
- 𝐶¹ pathological behavior: Pugh’s example 261272
- Bibliography 267278
- Index 273284 free
- Back Cover Back Cover1289

#### Readership

Graduate students interested in dynamical systems and ergodic theory and research mathematicians interested in smooth ergodic theory.