Nonuniform hyperbolicity : dynamics of systems with nonzero Lyapunov exponents
著者
書誌事項
Nonuniform hyperbolicity : dynamics of systems with nonzero Lyapunov exponents
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, 115）
Cambridge University Press, 2007
大学図書館所蔵 件 / 全49件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. 491-500) and index
内容説明・目次
内容説明
Designed to work as a reference and as a supplement to an advanced course on dynamical systems, this book presents a self-contained and comprehensive account of modern smooth ergodic theory. Among other things, this provides a rigorous mathematical foundation for the phenomenon known as deterministic chaos - the appearance of 'chaotic' motions in pure deterministic dynamical systems. A sufficiently complete description of topological and ergodic properties of systems exhibiting deterministic chaos can be deduced from relatively weak requirements on their local behavior known as nonuniform hyperbolicity conditions. Nonuniform hyperbolicity theory is an important part of the general theory of dynamical systems. Its core is the study of dynamical systems with nonzero Lyapunov exponents both conservative and dissipative, in addition to cocycles and group actions. The results of this theory are widely used in geometry (e.g., geodesic flows and Teichmuller flows), in rigidity theory, in the study of some partial differential equations (e.g., the Schroedinger equation), in the theory of billiards, as well as in applications to physics, biology, engineering, and other fields.
目次
- 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.
「Nielsen BookData」 より
