Nonuniformly Hyperbolic Attractors : Geometric and Probabilistic Aspects. 1st ed. 2020

種類:

電子ブック

責任表示:

by José F. Alves

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Alves, José F.
• SpringerLink (Online service)

シリーズ名:

Springer Monographs in Mathematics ;

ISBN:

9783030628147 [3030628140]    

注記:

1 Introduction -- 2 Preliminaries -- 3 Expanding Structures -- 4 Hyperbolic Structures -- 5 Inducing Schemes -- 6 Nonuniformly Expanding Attractors -- 7 Partially Hyperbolic Attractors -- Index.
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

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