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Nonuniformly Hyperbolic Attractors - Geometric and Probabilistic Aspects (Paperback, 1st ed. 2020)
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Nonuniformly Hyperbolic Attractors - Geometric and Probabilistic Aspects (Paperback, 1st ed. 2020)
Series: Springer Monographs in Mathematics
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This monograph offers a coherent, self-contained account of the
theory of Sinai-Ruelle-Bowen measures and decay of correlations for
nonuniformly hyperbolic dynamical systems. A central topic in the
statistical theory of dynamical systems, the book in particular
provides a detailed exposition of the theory developed by L.-S.
Young for systems admitting induced maps with certain analytic and
geometric properties. After a brief introduction and preliminary
results, Chapters 3, 4, 6 and 7 provide essentially the same
pattern of results in increasingly interesting and complicated
settings. Each chapter builds on the previous one, apart from
Chapter 5 which presents a general abstract framework to bridge the
more classical expanding and hyperbolic systems explored in
Chapters 3 and 4 with the nonuniformly expanding and partially
hyperbolic systems described in Chapters 6 and 7. Throughout the
book, the theory is illustrated with applications. A clear and
detailed account of topics of current research interest, this
monograph will be of interest to researchers in dynamical systems
and ergodic theory. In particular, beginning researchers and
graduate students will appreciate the accessible, self-contained
presentation.
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