Nonuniform Hyperbolicity: Dynamics of Systems with Nonzero Lyapunov Exponents by Luis BarreiraNonuniform Hyperbolicity: Dynamics of Systems with Nonzero Lyapunov Exponents by Luis Barreira

Nonuniform Hyperbolicity: Dynamics of Systems with Nonzero Lyapunov Exponents

byLuis Barreira, Yakov Pesin

Hardcover | September 3, 2007

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This book presents the theory of dynamical systems with nonzero Lyapunov exponents, offering a rigorous mathematical foundation for deterministic chaos - the appearance of "chaotic" motions in pure deterministic dynamical systems. These ideas and methods are used in many areas of mathematics as well as in physics, biology, and engineering. Despite the substantial amount of research on the subject, there have been relatively few attempts to summarize and unify results in a single manuscript. This comprehensive book can be used as a reference or as a supplement to an advanced course on dynamical systems.
Yakov Pesin is a Distinguished Professor of Mathematics at The Pennsylvania State University. He obtained his PhD from The Gorky State University in 1979. He is the author of three books, Dimension Theory in Dynamical Systems, Lectures on Partial Hyperbolicity and Stable Ergodicity, and, with Luis Barreira, Lyapunov Exponents and Smoot...
Title:Nonuniform Hyperbolicity: Dynamics of Systems with Nonzero Lyapunov ExponentsFormat:HardcoverDimensions:528 pages, 9.21 × 6.14 × 1.38 inPublished:September 3, 2007Publisher:Cambridge University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0521832586

ISBN - 13:9780521832588


Table of Contents

Part I. Linear Theory: 1. The concept of nonuniform hyperbolicity; 2. Lyapunov exponents for linear extensions; 3. Regularity of cocycles; 4. Methods for estimating exponents; 5. The derivative cocycle; Part II. Examples and Foundations of the Nonlinear Theory: 6. Examples of systems with hyperbolic behavior; 7. Stable manifold theory; 8. Basic properties of stable and unstable manifolds; Part III. Ergodic Theory of Smooth and SRB Measures: 9. Smooth measures; 10. Measure-theoretic entropy and Lyapunov exponents; 11. Stable ergodicity and Lyapunov exponents; 12. Geodesic flows; 13. SRB measures; Part IV. General Hyperbolic Measures: 14. Hyperbolic measures: entropy and dimension; 15. Hyperbolic measures: topological properties.