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Ergodic Theory, Hyperbolic Dynamics and Dimension Theory

  • Luis Barreira

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Luis Barreira
    Pages 1-16
  3. Ergodic Theory

    1. Front Matter
      Pages 17-17
    2. Luis Barreira
      Pages 19-64
    3. Luis Barreira
      Pages 65-103
  4. Entropy and Pressure

    1. Front Matter
      Pages 105-105
    2. Luis Barreira
      Pages 107-146
    3. Luis Barreira
      Pages 147-168
  5. Hyperbolic Dynamics

    1. Front Matter
      Pages 169-169
    2. Luis Barreira
      Pages 171-200
    3. Luis Barreira
      Pages 201-231
  6. Dimension Theory

    1. Front Matter
      Pages 233-233
    2. Luis Barreira
      Pages 235-251
    3. Luis Barreira
      Pages 253-275
  7. Back Matter
    Pages 277-290

About this book

Introduction

Over the last two decades, the dimension theory of dynamical systems has progressively developed into an independent and extremely active field of research. The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research: ergodic theory, hyperbolic dynamics, and dimension theory. It starts with the basic notions of the first two topics and ends with a sufficiently high-level introduction to the third. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory.

The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner. In particular, it can be used as a basis for graduate courses on any of these three subjects. The text can also be used for self-study: it is self-contained, and with the exception of some well-known basic facts from other areas, all statements include detailed proofs.

Keywords

37AXX, 37DXX, 37C45 dimension theory entropy theory ergodic theory hyperbolic dynamics thermodynamic formalism

Authors and affiliations

  • Luis Barreira
    • 1
  1. 1., Departamento de MatemáticaInstituto Superior TécnicoLisboaPortugal

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-28090-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-28089-4
  • Online ISBN 978-3-642-28090-0
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site
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