Skip to main content
  • Book
  • © 2013

Dimension Theory of Hyperbolic Flows

Authors:

  • 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 book series: Springer Monographs in Mathematics (SMM)

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (11 chapters)

  1. Front Matter

    Pages I-X
  2. Introduction

    • Luís Barreira
    Pages 1-15
  3. Basic Notions

    1. Front Matter

      Pages 17-17
    2. Suspension Flows

      • Luís Barreira
      Pages 19-32
    3. Hyperbolic Flows

      • Luís Barreira
      Pages 33-38
    4. Pressure and Dimension

      • Luís Barreira
      Pages 39-47
  4. Dimension Theory

    1. Front Matter

      Pages 49-49
    2. Dimension of Hyperbolic Sets

      • Luís Barreira
      Pages 51-59
    3. Pointwise Dimension and Applications

      • Luís Barreira
      Pages 61-77
  5. Multifractal Analysis

    1. Front Matter

      Pages 79-79
    2. Suspensions over Symbolic Dynamics

      • Luís Barreira
      Pages 81-90
    3. Multifractal Analysis of Hyperbolic Flows

      • Luís Barreira
      Pages 91-108
  6. Variational Principles

    1. Front Matter

      Pages 109-109
    2. Entropy Spectra

      • Luís Barreira
      Pages 111-125
    3. Multidimensional Spectra

      • Luís Barreira
      Pages 127-138
    4. Dimension Spectra

      • 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.

Authors and Affiliations

  • Instituto Superior Técnico, Departamento de Matemática, Universidade Técnica de Lisboa, Lisbon, Portugal

    Luís Barreira

About the author

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

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access