Lyapunov Exponents and Smooth Ergodic Theory
About this Title
Luis Barreira, Instituto Superior Técnico, Lisboa, Portugal and Yakov B. Pesin, Pennsylvania State University, University Park, PA
Publication: University Lecture Series
Publication Year 2002: Volume 23
ISBNs: 978-0-8218-2921-9 (print); 978-1-4704-2170-0 (online)
MathSciNet review: MR1862379
MSC: Primary 37D25; Secondary 34D08, 37C40, 37D10
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 non-trivial 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.
Graduate students and research mathematicians interested in dynamical systems and ergodic theory.
Table of Contents
- 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