Introduction to smooth ergodic theory / Luis Barreira and Yakov Pesin.
Material type:
TextSeries: Graduate studies in mathematics ; v 148.Publication details: Providence : American Mathematical Society, c2013.Description: ix, 277 p. : illustrations ; 26 cmISBN: - 9780821898536 (alk. paper)
- 515.48 23 B271
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 515.48 B271 (Browse shelf(Opens below)) | Available | 136159 |
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| 515.45 W926 Numerical Treatment of Integral Equations | 515.46 Y22 Half-discrete Hilbert-type inequalities / | 515.48 B151 Ergodic theory, open dynamics, and coherent structures / | 515.48 B271 Introduction to smooth ergodic theory / | 515.48 C854 Ergodic theory and dynamical systems / | 515.48 Ei35 Ergodic theory | 515.48 Ei36 Operator theoretic aspects of ergodic theory / |
Includes bibliographical references (pages 267-271) and index.
1. Examples of hyperbolic dynamical systems --
2. General theory of Lyapunov exponents --
3. Lyapunov stability theory of nonautonomous equations --
4. Elements of the nonuniform hyyperbolicity theory --
5. Cocycles over dynamical systems --
6. The multiplicative ergodic theorem --
7. Local manifold theory --
8. Absolute continuity of local manifolds --
9. Ergodic properties of smooth hyperbolic measures --
10. Geodesic flows on surfaces of nonpositive curvature --
11. Cone technics --
12. Partially hyperbolic diffeomorphisms with nonzero exponents --
13. More examples of dynamical systems with nonzero Lyapunov exponents --
14. Anosov rigidity --
15. C¹ pathological behavior: Pugh's example--
Bibliography--
Index.
The book consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential equations, the concept of nonuniform hyperbolicity, stable manifold theory (with emphasis on the absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. The authors also present a detailed description of all basic examples of conservative systems with nonzero Lyapunov exponents, including the geodesic flows on compact surfaces of nonpositive curvature. This book is aimed at graduate students specialising in dynamical systems and ergodic theory as well as anyone who wants to acquire a working knowledge of smooth ergodic theory and to learn how to use its tools. With more than 80 exercises, the book can be used as a primary textbook for an advanced course in smooth ergodic theory.
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