© 2013

Dimension Theory of Hyperbolic Flows

  • First comprehensive exposition of dimension theory of hyperbolic flows

  • Includes an overview of dimension theory and multifractal analysis

  • Includes a detailed discussion of major open problems in the area


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

Table of contents

  1. Front Matter
    Pages I-X
  2. Luís Barreira
    Pages 1-15
  3. Basic Notions

    1. Front Matter
      Pages 17-17
    2. Luís Barreira
      Pages 19-32
    3. Luís Barreira
      Pages 33-38
    4. Luís Barreira
      Pages 39-47
  4. Dimension Theory

    1. Front Matter
      Pages 49-49
    2. Luís Barreira
      Pages 51-59
    3. Luís Barreira
      Pages 61-77
  5. Multifractal Analysis

    1. Front Matter
      Pages 79-79
    2. Luís Barreira
      Pages 81-90
    3. Luís Barreira
      Pages 91-108
  6. Variational Principles

    1. Front Matter
      Pages 109-109
    2. Luís Barreira
      Pages 111-125
    3. Luís Barreira
      Pages 127-138
    4. Luís Barreira
      Pages 139-149
  7. Back Matter
    Pages 151-158

About this book


The dimension theory of dynamical systems has progressively developed, especially over the last two decades, into an independent and extremely active field of research. Its main aim is to study the complexity of sets and measures that are invariant under the dynamics. In particular, it is essential to characterizing chaotic strange attractors. To date, some parts of the theory have either only been outlined, because they can be reduced to the case of maps, or are too technical for a wider audience. In this respect, the present monograph is intended to provide a comprehensive guide. Moreover, the text is self-contained and with the exception of some basic results in Chapters 3 and 4, all the results in the book include detailed proofs.
The book is intended for researchers and graduate students specializing in dynamical systems who wish to have a sufficiently comprehensive view of the theory together with a working knowledge of its main techniques. The discussion of some open problems is also included in the hope that it may lead to further developments. Ideally, readers should have some familiarity with the basic notions and results of ergodic theory and hyperbolic dynamics at the level of an introductory course in the area, though the initial chapters also review all the necessary material.


37C45, 37Dxx, 37Axx Markov systems dimension theory hyperbolic flows multifractal analysis variational principles

Authors and affiliations

  1. 1.Instituto Superior Técnico, Departamento de MatemáticaUniversidade Técnica de LisboaLisbonPortugal

About the authors

Luis Barreira is a Professor of Mathematics at the Instituto Superior Técnico in Lisbon. He is the author of 17 books, including several textbooks published in several languages, and more than 100 articles on mathematics, mainly on differential equations, dynamical systems and ergodic theory.

Bibliographic information

  • Book Title Dimension Theory of Hyperbolic Flows
  • Authors Luís Barreira
  • Series Title Springer Monographs in Mathematics
  • Series Abbreviated Title Springer Monographs in Mathematics
  • DOI
  • Copyright Information Springer International Publishing Switzerland 2013
  • Publisher Name Springer, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-00547-8
  • Softcover ISBN 978-3-319-03392-1
  • eBook ISBN 978-3-319-00548-5
  • Series ISSN 1439-7382
  • Edition Number 1
  • Number of Pages X, 158
  • 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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