Lyapunov exponents and smooth ergodic theory. (English) Zbl 1195.37002

University Lecture Series 23. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-2921-1/pbk). xii, 151 p. (2001).
This book is a revised and expanded version of the authors’ 86-page survey [in: Smooth ergodic theory and its applications. Proceedings of the AMS summer research institute, Seattle, WA, USA, July 26-August 13, 1999. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Pure Math. 69, 3–106 (2001; Zbl 0996.37001)]. For the content, we may refer to the review there; the main differences are that this book contains more examples of dynamical systems with nonzero Lyapunov exponents, and that many proofs are given here in full detail.


37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37A30 Ergodic theorems, spectral theory, Markov operators


Zbl 0996.37001