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- DescriptionDesigned to work as a reference and as a supplement to an advanced course on dynamical systems, this book presents a self-contained and comprehensive account of modern smooth ergodic theory. Among other things, this provides a rigorous mathematical foundation for the phemen kwn as deterministic chaos - the appearance of 'chaotic' motions in pure deterministic dynamical systems. A sufficiently complete description of topological and ergodic properties of systems exhibiting deterministic chaos can be deduced from relatively weak requirements on their local behavior kwn as nuniform hyperbolicity conditions. Nonuniform hyperbolicity theory is an important part of the general theory of dynamical systems. Its core is the study of dynamical systems with nzero Lyapuv exponents both conservative and dissipative, in addition to cocycles and group actions. The results of this theory are widely used in geometry (e.g., geodesic flows and Teichmuller flows), in rigidity theory, in the study of some partial differential equations (e.g., the Schrodinger equation), in the theory of billiards, as well as in applications to physics, biology, engineering, and other fields.
- Author BiographyLuis Barreira is a Professor of Mathematics at Instituto Superior Tecnico in Lisbon. He obtained his PhD from The Pennsylvania State University in 1996, under the guidance of Yakov Pesin, with whom he co-authored the book Lyapunov Exponents and Smooth Ergodic Theory. He has also written two surveys and more than forty research papers in dynamical systems. Yakov Pesin is a Distinguished Professor of Mathematics at The Pennsylvania State University. He obtained his PhD from The Gorky State University in 1979. He is the author of three books, Dimension Theory in Dynamical Systems, Lectures on Partial Hyperbolicity and Stable Ergodicity, and, with Luis Barreira, Lyapunov Exponents and Smooth Ergodic Theory, as well as six surveys and more than seventy research papers. He is an executive editor of the journal Ergodic Theory and Dynamical Systems.
- Author(s)Anatole Katok,Luis Barreira,Yakov Pesin
- PublisherCambridge University Press
- Date of Publication03/09/2007
- SubjectScience & Mathematics: Textbooks & Study Guides
- Series TitleEncyclopedia of Mathematics and Its Applications
- Series Part/Volume NumberNo. 115
- Place of PublicationCambridge
- Country of PublicationUnited Kingdom
- ImprintCambridge University Press
- Content NoteIllustrations
- Weight990 g
- Width156 mm
- Height234 mm
- Spine33 mm
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