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Dimension and Recurrence in Hyperbolic Dynamics

  • Luis Barreira

Part of the Progress in Mathematics book series (PM, volume 272)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Introduction

    1. Pages 1-5
  3. Basic Notions

    1. Pages 7-15
  4. Dimension Theory

  5. Multifractal Analysis: Core Theory

  6. Multifractal Analysis: Further Developments

    1. Front Matter
      Pages 165-165
    2. Pages 191-208
  7. Hyperbolicity and Recurrence

  8. Back Matter
    Pages 285-300

About this book

Introduction

The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It includes the discussion of the foundations, main results, and main techniques in the rich interplay of four main areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. It also gives a panorama of several selected topics of current research interest. More than half of the material appears here for the first time in book form, describing many recent developments in the area such as topics on irregular sets, variational principles, applications to number theory, measures of maximal dimension, multifractal nonrigidity, and quantitative recurrence. All the results are included with detailed proofs, many of them simplified or rewritten on purpose for the book.

The text is self-contained and directed to researchers as well as graduate students that wish to have a global view of the theory together with a working knowledge of its main techniques. It will also be useful as as basis for graduate courses in dimension theory of dynamical systems, multifractal analysis, and pointwise dimension and recurrence in hyperbolic dynamics.

Keywords

calculus dimension theory hyperbolic set maximum multifractal analysis recurrence symbolic dynamics

Authors and affiliations

  • Luis Barreira
    • 1
  1. 1.Departmento de MatemáticaInstituto Superior TécnicoLisboaPortugal

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-7643-8882-9
  • Copyright Information Birkhäuser Basel 2008
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-7643-8881-2
  • Online ISBN 978-3-7643-8882-9
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site