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Smooth ergodic theory and its applications : [electronic resource] proceedings of the AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications, July 26-August 13, 1999, University of Washington, Seattle / Anatole Katok ... [et al.], editors.

By: AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications (1999 : University of Washington)Contributor(s): Katok, A. BMaterial type: Text

TextSeries: Proceedings of symposia in pure mathematics ; v. 69Publication details: Providence, R.I. : American Mathematical Society, c2001Description: 1 online resource (x, 881 p. : ill.)ISBN: 9780821893746 (online)Subject(s): Ergodic theory -- CongressesAdditional physical formats: Smooth ergodic theory and its applications :DDC classification: 515/.42 LOC classification: QA611.5 | .A475 1999Online resources: Contents | Contents

Contents:

Lectures on Lyapunov exponents and smooth ergodic theory / L. Barreira and Ya. Pesin -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858534 Appendix A: H�older continuity of invariant distributions / M. Brin -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858534-a Appendix B: An example of a smooth hyperbolic measure with countably many ergodic components / D. Dolgopyat, H. Hu and Ya Pesin -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858534-b Cocycles, cohomology and combinatorial constructions in ergodic theory / Anatole Katok -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858535 A tutorial on KAM theory / Rafael de la Llave -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858536 Decay of correlations / Viviane Baladi -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858537 Recent results about stable ergodicity / Keith Burns, Charles Pugh, Michael Shub and Amie Wilkinson -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858538 Statistical properties of some almost hyperbolic systems / Huyi Hu -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858539 Random $f$-expansions / Yuri Kifer -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858540 Dynamical zeta functions / Mark Pollicott -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858541 An overview of the dimension theory of dynamical systems / J�org Schmeling and Howard Weiss -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858542 Collet-Eckmann condition in one-dimensional dynamics / Grzegorz �Swiatek -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858543 Monotonicity, $\mathcal {J}$-algebra of Potapov and Lyapunov exponents / Maciej P. Wojtkowski -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858544 Geodesic flows in manifolds of nonpositive curvature / Patrick Eberlein -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858545 Closed geodesics and the uniqueness of the maximal measure for rank 1 geodesic flows / Gerhard Knieper -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858546 Invariant measures for actions of higher rank abelian groups / Boris Kalinin and Anatole Katok -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858547 Some applications of homogeneous dynamics to number theory / Dmitry Kleinbock -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858548 Measurable rigidity of algebraic $\mathbb {Z}^d$-actions / Klaus Schmidt -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858549 Almost reducibility of linear quasi-periodic systems / L. H. Eliasson -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858550 A lecture on the classical KAM theorem / J�urgen P�oschel -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858551 A Lagrangian proof of the invariant curve theorem for twist mappings / M. Levi and J. Moser -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858552 Thermodynamical formalism for piecewise invertible maps: absolutely continuous invariant measures as equilibrium states / J�er�ome Buzzi -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858553 Smoothness of holonomy maps derived from unstable foliation / M. Guysinsky -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858554 Schr�odinger operators and topological pressure on manifolds of negative curvature / Viorel Ni�tic�a and Frederico Xavier -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858555 Isoperimetric and ergodic properties of horospheres in symmetric spaces / Norbert Peyerimhoff -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858556 Minimal but not uniquely ergodic diffeomorphisms / Alistair Windsor -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858557 Piecewise smooth maps with absolutely continuous invariant measures and uniformly scaled Markov partitions / Michael Jakobson -- http://www.ams.org/pspum/069 http://dx.doi.org/10.1090/pspum/069/1858558

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Includes bibliographical references.

Lectures on Lyapunov exponents and smooth ergodic theory / L. Barreira and Ya. Pesin -- Appendix A: H�older continuity of invariant distributions / M. Brin -- Appendix B: An example of a smooth hyperbolic measure with countably many ergodic components / D. Dolgopyat, H. Hu and Ya Pesin -- Cocycles, cohomology and combinatorial constructions in ergodic theory / Anatole Katok -- A tutorial on KAM theory / Rafael de la Llave -- Decay of correlations / Viviane Baladi -- Recent results about stable ergodicity / Keith Burns, Charles Pugh, Michael Shub and Amie Wilkinson -- Statistical properties of some almost hyperbolic systems / Huyi Hu -- Random $f$-expansions / Yuri Kifer -- Dynamical zeta functions / Mark Pollicott -- An overview of the dimension theory of dynamical systems / J�org Schmeling and Howard Weiss -- Collet-Eckmann condition in one-dimensional dynamics / Grzegorz �Swiatek -- Monotonicity, $\mathcal {J}$-algebra of Potapov and Lyapunov exponents / Maciej P. Wojtkowski -- Geodesic flows in manifolds of nonpositive curvature / Patrick Eberlein -- Closed geodesics and the uniqueness of the maximal measure for rank 1 geodesic flows / Gerhard Knieper -- Invariant measures for actions of higher rank abelian groups / Boris Kalinin and Anatole Katok -- Some applications of homogeneous dynamics to number theory / Dmitry Kleinbock -- Measurable rigidity of algebraic $\mathbb {Z}^d$-actions / Klaus Schmidt -- Almost reducibility of linear quasi-periodic systems / L. H. Eliasson -- A lecture on the classical KAM theorem / J�urgen P�oschel -- A Lagrangian proof of the invariant curve theorem for twist mappings / M. Levi and J. Moser -- Thermodynamical formalism for piecewise invertible maps: absolutely continuous invariant measures as equilibrium states / J�er�ome Buzzi -- Smoothness of holonomy maps derived from unstable foliation / M. Guysinsky -- Schr�odinger operators and topological pressure on manifolds of negative curvature / Viorel Ni�tic�a and Frederico Xavier -- Isoperimetric and ergodic properties of horospheres in symmetric spaces / Norbert Peyerimhoff -- Minimal but not uniquely ergodic diffeomorphisms / Alistair Windsor -- Piecewise smooth maps with absolutely continuous invariant measures and uniformly scaled Markov partitions / Michael Jakobson --