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vls/2603nrwcece.visuallibrary.netvdIntroduction to smooth ergodic theoryBarreira, LuisautPesin, Yakov B.auttextbookProvidence, Rhode IslandAmerican Mathematical Society[2023]2023Second editionmonographicengxv, 336 SeitenIllustrationenThis 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 absolute continuity of invariant foliations), and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. A detailed description of all the basic examples of conservative systems with nonzero Lyapunov exponents, including the geodesic flows on compact surfaces of nonpositive curvature, is also presented. There are more than 80 exercises. The book is aimed at graduate students specializing in dynamical systems and ergodic theory as well as anyone who wishes to get a working knowledge of smooth ergodic theory and to learn how to use its tools. It can also be used as a source for special topics courses on nonuniform hyperbolicity. The only prerequisite for using this book is a basic knowledge of real analysis, measure theory, differential equations, and topology, although the necessary background definitions and results are provided.In this second edition, the authors improved the exposition and added more exercises to make the book even more student-oriented. They also added new material to bring the book more in line with the current research in dynamical systems.Luís Barreira, Yakov PesinIncludes bibliographical references and indexDynamical systems and ergodic theory -- Dynamical systems with hyperbolic behavior -- Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)Dynamical systems and ergodic theory -- Smooth dynamical systems: general theory -- Smooth ergodic theory, invariant measures31.70KXP1832134865978-1-4704-7065-4978-1-4704-7307-5HT030335306Graduate studies in mathematics231HT004977518Online-Ausgabe978147047306820230817202407252544964rda https://ce.visuallibrary.net//domainresource/static/graphics/connectors/viewerLogo.gif http://193.30.112.129:83/F/?func=find-c&ccl_term=ICS%3D2544964 https://ce.visuallibrary.net/id/1296230 https://ce.visuallibrary.net/i3f/v20/1296230/manifest https://ce.visuallibrary.net/proto_ftsearch/1296230