**University Lecture Series**

Volume: 23;
2002;
151 pp;
Softcover

MSC: Primary 37;

Print ISBN: 978-0-8218-2921-9

Product Code: ULECT/23

List Price: $36.00

Individual Member Price: $28.80

**Electronic ISBN: 978-1-4704-2170-0
Product Code: ULECT/23.E**

List Price: $36.00

Individual Member Price: $28.80

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# Lyapunov Exponents and Smooth Ergodic Theory

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*Luis Barreira; Yakov B. Pesin*

This book is a systematic introduction to smooth ergodic theory. The topics
discussed include the general (abstract) theory of Lyapunov exponents and its
applications to the stability theory of differential equations, stable manifold
theory, absolute continuity, and the ergodic theory of dynamical systems with
nonzero Lyapunov exponents (including geodesic flows).

The authors consider several nontrivial examples of dynamical systems with
nonzero Lyapunov exponents to illustrate some basic methods and ideas of the
theory.

This book is self-contained. The reader needs a basic knowledge of real
analysis, measure theory, differential equations, and topology. The authors
present basic concepts of smooth ergodic theory and provide complete proofs of
the main results. They also state some more advanced results to give readers a
broader view of smooth ergodic theory. This volume may be used by those
nonexperts who wish to become familiar with the field.

#### Table of Contents

# Table of Contents

## Lyapunov Exponents and Smooth Ergodic Theory

- Cover Cover11 free
- Title v6 free
- Copyright vi7 free
- Contents ix10 free
- Preface xi12 free
- Introduction 114 free
- Chapter 1. Lyapunov Stability Theory of Differential Equations 518 free
- Chapter 2. Elements of Nonuniform Hyperbolic Theory 3548
- Chapter 3. Examples of Nonuniformly Hyperbolic Systems 6174
- Chapter 4. Local Manifold Theory 8194
- Chapter 5. Ergodic Properties of Smooth Hyperbolic Measures 115128
- 5.1. Absolute Continuity and Smooth Invariant Measures 115128
- 5.2. Ergodicity of Smooth Hyperbolic Measures 117130
- 5.3. Local Ergodicity 122135
- 5.4. The Entropy Formula 130143
- 5.5. SRB-Measures and General Hyperbolic Measures 138151
- 5.6. Geodesic Flows on Compact Surfaces of Nonpositive Curvature 140153

- Bibliography 145158
- Index 147160
- Back Cover Back Cover1166

#### Readership

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

#### Reviews

Even though there are a very great number of publications on this subject, the book from Barreira and Pesin in the first comprehensive textbook. It is highly worth recommending both to advanced and interested students and to scientists working on dynamical systems … The book is self-contained and gets by to a great extent without additional references. It has a clear and well thought-out structure and forgoes any unnecessary complexity of notation.

-- translated from Jahresbericht der Deutschen Mathematiker-Vereinigung

Compact and useful self-contained book … a rich array of examples … this is a handy and lucid book on a tricky subject.

-- Mathematical Reviews