Introduction to Smooth Ergodic Theory
American Mathematical Society (Verlag)
978-0-8218-9853-6 (ISBN)
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. The book is self-contained and only a basic knowledge of real analysis, measure theory, differential equations, and topology is required and, even so, the authors provide the reader with the necessary background definitions and results.
Luis Barreira, Instituto Superior Tecnico, Lisbon, Portugal. Yakov Pesin, Pennsylvania State University, State College, PA, USA.
Preface
Part I. The core of the theory
Examples of hyperbolic dynamical systems
General theory of Lyapunov exponents
Lyapunov stability theory of nonautonomous equations
Elements of the nonuniform hyperbolicity theory
Cocycles over dynamical systems
The Multiplicative Ergodic Theorem
Local manifold theory
Absolute continuity of local manifolds
Ergodic properties of smooth hyperbolic measures
Geodesic flows on surfaces of nonpositive curvature
Part II. Selected advanced topics
Cone technics
Partially hyperbolic diffeomorphisms with nonzero exponents
More examples of dynamical systems with nonzero Lyapunov exponents
Anosov rigidity
𝐶¹ pathological behavior: Pugh’s example
Bibliography
Index
Erscheint lt. Verlag | 30.7.2013 |
---|---|
Reihe/Serie | Graduate Studies in Mathematics |
Verlagsort | Providence |
Sprache | englisch |
Gewicht | 663 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 0-8218-9853-1 / 0821898531 |
ISBN-13 | 978-0-8218-9853-6 / 9780821898536 |
Zustand | Neuware |
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