Nonuniform Hyperbolicity Dynamics of Systems with Nonzero Lyapunov Exponents 1st Edition by Luis Barreira, Yakov Pesin ISBN 0521832586 9780521832588

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Product details:

ISBN 10: 0521832586

ISBN 13: 9780521832588 

Author: Luis Barreira, Yakov Pesin 

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.

Table of contents:

Part I. Linear Theory
1.1 The concept of nonuniform hyperbolicity
1.2 Lyapunov exponents for linear extensions
1.3 Regularity of cocycles
1.4 Methods for estimating exponents
1.5 The derivative cocycle

Part II. Examples and Foundations of the Nonlinear Theory
2.1 Examples of systems with hyperbolic behavior
2.2 Stable manifold theory
2.3 Basic properties of stable and unstable manifolds

Part III. Ergodic Theory of Smooth and SRB Measures
3.1 Smooth measures
3.2 Measure-theoretic entropy and Lyapunov exponents
3.3 Stable ergodicity and Lyapunov exponents
3.4 Geodesic flows
3.5 SRB measures

Part IV. General Hyperbolic Measures
4.1 Hyperbolic measures: entropy and dimension
4.2 Hyperbolic measures: topological properties

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Tags: Luis Barreira, Yakov Pesin, Nonuniform, Hyperbolicity, Dynamics, Lyapunov Exponents