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© 2011

Thermodynamic Formalism and Applications to Dimension Theory

Benefits

  • First comprehensive exposition of several main extensions of the thermodynamic formalism.

  • The emphasis of the text is on the relation to dimension theory and multifractal analysis.

  • Includes a discussion of very recent results in the area as well as some open problems.

  • The text is self-contained and all the results are included with detailed proofs.

Book

Part of the Progress in Mathematics book series (PM, volume 294)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Luis Barreira
    Pages 1-16
  3. Classical Thermodynamic Formalism

    1. Front Matter
      Pages 17-17
    2. Luis Barreira
      Pages 19-40
    3. Luis Barreira
      Pages 41-52
  4. Nonadditive Thermodynamic Formalism

    1. Front Matter
      Pages 53-53
    2. Luis Barreira
      Pages 55-83
    3. Luis Barreira
      Pages 85-119
    4. Luis Barreira
      Pages 121-138
  5. Subadditive Thermodynamic Formalism

    1. Front Matter
      Pages 139-139
    2. Luis Barreira
      Pages 141-164
    3. Luis Barreira
      Pages 165-178
    4. Luis Barreira
      Pages 179-199
  6. Almost Additive Thermodynamic Formalism

    1. Front Matter
      Pages 201-201
    2. Luis Barreira
      Pages 203-229
    3. Luis Barreira
      Pages 231-253
    4. Luis Barreira
      Pages 255-280
  7. Back Matter
    Pages 281-297

About this book

Introduction

This self-contained monograph presents a unified exposition of the thermodynamic formalism and some of its main extensions, with emphasis on the relation to dimension theory and multifractal analysis of dynamical systems. In particular, the book considers three different flavors of the thermodynamic formalism, namely nonadditive, subadditive, and almost additive, and provides a detailed discussion of some of the most significant results in the area, some of them quite recent. It also includes a discussion of the most substantial applications of these flavors of the thermodynamic formalism to dimension theory and multifractal analysis of dynamical systems.

Keywords

dimension theory multifractal analysis thermodynamic formalism

Authors and affiliations

  1. 1.Instituto Superior Tecnico, Depto. MatematicaUniversidade Tecnica LisboaLisboaPortugal

Bibliographic information

  • Book Title Thermodynamic Formalism and Applications to Dimension Theory
  • Authors Luis Barreira
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI https://doi.org/10.1007/978-3-0348-0206-2
  • Copyright Information Springer Basel AG 2011
  • Publisher Name Springer, Basel
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-0348-0205-5
  • Softcover ISBN 978-3-0348-0336-6
  • eBook ISBN 978-3-0348-0206-2
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages XII, 300
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Dynamical Systems and Ergodic Theory
  • Buy this book on publisher's site
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Reviews

From the reviews:

“This book gives a detailed account of the connection between two areas of dynamical systems, the thermodynamic formalism and dimension theory in dynamical systems. … The book is probably best read by someone already familiar with the basics of ergodic theory, dynamical systems, and the Hausdorff dimension … . the book gives the reader a good grounding in both thermodynamical formalism and applying the thermodynamic formalism to prove results in the dimension theory of dynamical systems.” (Thomas Michael Jordan, Mathematical Reviews, March, 2014)