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Nonuniformly Hyperbolic Attractors

Geometric and Probabilistic Aspects

  • Book
  • © 2020

Overview

Authors:
  1. José F. Alves

    1. Department of Mathematics, University of Porto, Porto, Portugal

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  • Provides a self-contained introduction to the theory of Young towers for dynamical systems with inducing schemes
  • Collects recent results on nonuniformly expanding maps and partially hyperbolic diffeomorphisms
  • Includes a detailed account of Gibbs–Markov maps

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Introduction

    • José F. Alves
    Pages 1-8

  3. Preliminaries

    • José F. Alves
    Pages 9-22

  4. Expanding Structures

    • José F. Alves
    Pages 23-101

  5. Hyperbolic Structures

    • José F. Alves
    Pages 103-159

  6. Inducing Schemes

    • José F. Alves
    Pages 161-187

  7. Nonuniformly Expanding Attractors

    • José F. Alves
    Pages 189-223

  8. Partially Hyperbolic Attractors

    • José F. Alves
    Pages 225-256

  9. Back Matter

    Pages 257-259
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Keywords

About this book

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 topicsof 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.

Authors and Affiliations

  • Department of Mathematics, University of Porto, Porto, Portugal

    José F. Alves

About the author

José Ferreira Alves is a full Professor at the Department of Mathematics of the Faculty of Sciences of the University of Porto, Portugal. He obtained his PhD in Mathematics from the Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro (Brazil), in 1997. In 2000, he was a postdoc at the University of Maryland, USA, and during the academic year 2018/19 he was a Visiting Professor at Loughborough University, UK, with a grant from the Leverhulme Trust. His research interests lie in Dynamical Systems and Ergodic Theory, with an emphasis on the statistical properties of nonuniformly hyperbolic dynamics.

Bibliographic Information

  • Book Title: Nonuniformly Hyperbolic Attractors

  • Book Subtitle: Geometric and Probabilistic Aspects

  • Authors: José F. Alves

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-62814-7

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

  • Hardcover ISBN: 978-3-030-62813-0Published: 20 December 2020

  • Softcover ISBN: 978-3-030-62816-1Published: 20 December 2021

  • eBook ISBN: 978-3-030-62814-7Published: 19 December 2020

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XI, 259

  • Number of Illustrations: 5 b/w illustrations

  • Topics: Dynamical Systems and Ergodic Theory, Vibration, Dynamical Systems, Control

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