Notices of the American Mathematical Society

This book is the first comprehensive introduction to smooth ergodic theory. It consists of two parts: the first introduces the core of the theory and the second discusses more advanced topics. In particular, the book describes the general theory of Lyapunov exponents and its applications to the stability theory of differential equations, the concept of nonuniform hyperbolicity, stable manifold theory (with emphasis on the absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. The authors also present a detailed description of all basic examples of conservative systems with nonzero Lyapunov exponents, including the geodesic flows on compact surfaces of nonpositive curvature. This book is a revised and considerably expanded version of the previous book by the same authors Lyapunov Exponents and Smooth Ergodic Theory (University Lecture Series, Vol. 23, AMS, 2002). It is aimed at graduate students specializing 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. May 2014 Front cover Hindawi Publishing AMS Mathematical Imagery WebAssign May 2014 Table of Contents AMS Community Network Princeton University Press Letters to the Editor Call for Applications & Nominations for Chief Editor of the Notices Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance, D. H. Bailey, J. M. Borwein, M. L. de Prada, Q. J. Zhu A Tribute to Hans Grauert, Alan Huckleberry and Thomas Peternell, coordinating editors AMS MathSciNet for Developing Countries Is Big Data Enough? A Reflection on the Changing Role of Mathematics in Applications, Domenico Napoletani, Marco Panza, Daniele Struppa AMS Book and Journal Donation Program WHAT IS..a Spectrahedron?, Cynthia Vinzant The New York Times Book of Mathematics--A Book Review, Reviewed by Ian Stewart AMS Award for Mathematics Programs That Make a Difference-Call for Nominations Sarnak Awarded 2014 Wolf prize Faltings Awarded Faisal Prize MAA Mathfest, August 6-9, 2014 Meeting the Challenges of Improved Post-Secondary Education in the Mathematical Sciences, David M. Bressoud, Eric M. Friedlander, C. David Levermore The Chinese Hedgehog and the American Fox: An Invitation to Dialogue, Mark Saul; and Marc Yor (1949-2014), Jean-Francois Le Gall and Jim Pitman Happy 91st, Cathleen Synge Morawetz, Allyn Jackson Doceamus: Listening to Teachers, Priscilla Bremser 2014 Award for Impact on the Teaching and Learning of Mathematics 2014 Award for an Exemplary Program or Achievement in a Mathematics Department Creative Streak: Williams College Math Department Wins National AMS Award, Allyn Jackson 2014 JPBM Communications Award MAA Awards Given in Baltimore AWM Awards Given in Baltimore 2014 Mathematics Programs That Make a Difference Mathematics People Mathematics Opportunities Inside the AMS Reference and Book List American Mathematical Society--Contributions Call for Nominations for the George David Birkhoff and Ruth Lyttle Satter Prizes, the Frank Nelson Cole Prize in Algebra, and the Levi L. Conant and the Albert Leon Whiteman Memorial Prizes Call for Nominations for the 2015 Frank and Brennie Morgan AMS-MAA-SIAM Prize Mathematics Calendar New Publications Offered by the AMS Classified Advertisements Meetings & Conferences of the AMS Meetings & Conferences Table of Contents Hindawi Publishing AMS Graduate Studies in Mathematics Series