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Lyapunov Exponents and Smooth Ergodic Theory

Luis Barreira Instituto Superior Técnico, Lisboa, Portugal
Yakov B. Pesin Pennsylvania State University, University Park, PA
Available Formats:
Softcover ISBN: 978-0-8218-2921-9
Product Code: ULECT/23
151 pp
List Price: $39.00 MAA Member Price:$35.10
AMS Member Price: $31.20 Electronic ISBN: 978-1-4704-2170-0 Product Code: ULECT/23.E 151 pp List Price:$36.00
MAA Member Price: $32.40 AMS Member Price:$28.80
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $58.50 MAA Member Price:$52.65
AMS Member Price: $46.80 Click above image for expanded view Lyapunov Exponents and Smooth Ergodic Theory Luis Barreira Instituto Superior Técnico, Lisboa, Portugal Yakov B. Pesin Pennsylvania State University, University Park, PA Available Formats:  Softcover ISBN: 978-0-8218-2921-9 Product Code: ULECT/23 151 pp  List Price:$39.00 MAA Member Price: $35.10 AMS Member Price:$31.20
 Electronic ISBN: 978-1-4704-2170-0 Product Code: ULECT/23.E 151 pp
 List Price: $36.00 MAA Member Price:$32.40 AMS Member Price: $28.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$58.50
MAA Member Price: $52.65 AMS Member Price:$46.80
• Book Details

University Lecture Series
Volume: 232002
MSC: Primary 37;

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.

Readership

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

• Table of Contents

• Chapters
• Introduction
• Chapter 1. Lyapunov stability theory of differential equations
• Chapter 2. Elements of nonuniform hyperbolic theory
• Chapter 3. Examples of nonuniformly hyperbolic systems
• Chapter 4. Local manifold theory
• Chapter 5. Ergodic properties of smooth hyperbolc measures
• 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
• Request Review Copy
• Get Permissions
Volume: 232002
MSC: Primary 37;

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.

Readership

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

• Chapters
• Introduction
• Chapter 1. Lyapunov stability theory of differential equations
• Chapter 2. Elements of nonuniform hyperbolic theory
• Chapter 3. Examples of nonuniformly hyperbolic systems
• Chapter 4. Local manifold theory
• Chapter 5. Ergodic properties of smooth hyperbolc measures
• 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
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