# Smooth Ergodic Theory and Its Applications

### About this Title

**Anatole Katok**, *Pennsylvania State University, University Park, PA*, **Rafael de la Llave**, *University of Texas at Austin, Austin, TX*, **Yakov Pesin**, *Pennsylvania State University, University Park, PA* and **Howard Weiss**, *Pennsylvania State University, University Park, PA*, Editors

Publication: Proceedings of Symposia in Pure Mathematics

Publication Year:
2001; Volume 69

ISBNs: 978-0-8218-2682-9 (print); 978-0-8218-9374-6 (online)

DOI: https://doi.org/10.1090/pspum/069

MathSciNet review: 1858533

MSC: Primary 37-06

### Table of Contents

**Front/Back Matter**

- L. Barreira and Ya. Pesin – Lectures on Lyapunov exponents and smooth ergodic theory [MR 1858534]
- M. Brin – Appendix A: Hölder continuity of invariant distributions [MR 1858534-a]
- D. Dolgopyat, H. Hu and Ya Pesin – Appendix B: An example of a smooth hyperbolic measure with countably many ergodic components [MR 1858534-b]
- Anatole Katok – Cocycles, cohomology and combinatorial constructions in ergodic theory [MR 1858535]
- Rafael de la Llave – A tutorial on KAM theory [MR 1858536]

** Part II. Survey-expository articles **

** Part IIa. Systems with hyperbolic behavior **

- Viviane Baladi – Decay of correlations [MR 1858537]
- Keith Burns, Charles Pugh, Michael Shub and Amie Wilkinson – Recent results about stable ergodicity [MR 1858538]
- Huyi Hu – Statistical properties of some almost hyperbolic systems [MR 1858539]
- Yuri Kifer – Random $f$-expansions [MR 1858540]
- Mark Pollicott – Dynamical zeta functions [MR 1858541]
- Jörg Schmeling and Howard Weiss – An overview of the dimension theory of dynamical systems [MR 1858542]
- Grzegorz Światek – Collet-Eckmann condition in one-dimensional dynamics [MR 1858543]
- Maciej P. Wojtkowski – Monotonicity, $\mathcal {J}$-algebra of Potapov and Lyapunov exponents [MR 1858544]

- Patrick Eberlein – Geodesic flows in manifolds of nonpositive curvature [MR 1858545]
- Gerhard Knieper – Closed geodesics and the uniqueness of the maximal measure for rank 1 geodesic flows [MR 1858546]

** Part IIc. Algebraic systems and rigidity **

- Boris Kalinin and Anatole Katok – Invariant measures for actions of higher rank abelian groups [MR 1858547]
- Dmitry Kleinbock – Some applications of homogeneous dynamics to number theory [MR 1858548]
- Klaus Schmidt – Measurable rigidity of algebraic $\mathbb {Z}^d$-actions [MR 1858549]

- L. H. Eliasson – Almost reducibility of linear quasi-periodic systems [MR 1858550]
- Jürgen Pöschel – A lecture on the classical KAM theorem [MR 1858551]
- M. Levi and J. Moser – A Lagrangian proof of the invariant curve theorem for twist mappings [MR 1858552]

- Jérôme Buzzi – Thermodynamical formalism for piecewise invertible maps: absolutely continuous invariant measures as equilibrium states [MR 1858553]
- M. Guysinsky – Smoothness of holonomy maps derived from unstable foliation [MR 1858554]
- Viorel Niţică and Frederico Xavier – Schrödinger operators and topological pressure on manifolds of negative curvature [MR 1858555]
- Norbert Peyerimhoff – Isoperimetric and ergodic properties of horospheres in symmetric spaces [MR 1858556]
- Alistair Windsor – Minimal but not uniquely ergodic diffeomorphisms [MR 1858557]
- Michael Jakobson – Piecewise smooth maps with absolutely continuous invariant measures and uniformly scaled Markov partitions [MR 1858558]