Dynamical Systems

An Introduction

  • Luis Barreira
  • Claudia Valls

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Luis Barreira, Claudia Valls
    Pages 1-6
  3. Luis Barreira, Claudia Valls
    Pages 7-25
  4. Luis Barreira, Claudia Valls
    Pages 27-56
  5. Luis Barreira, Claudia Valls
    Pages 57-86
  6. Luis Barreira, Claudia Valls
    Pages 87-112
  7. Luis Barreira, Claudia Valls
    Pages 113-151
  8. Luis Barreira, Claudia Valls
    Pages 153-179
  9. Luis Barreira, Claudia Valls
    Pages 181-202
  10. Back Matter
    Pages 203-209

About this book

Introduction

The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics. Dynamical Systems: An Introduction undertakes the difficult task to provide a self-contained and compact introduction.

Topics covered include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as a brief introduction to ergodic theory. In particular, the authors consider topological recurrence, topological entropy, homeomorphisms and diffeomorphisms of the circle, Sharkovski's ordering, the Poincaré-Bendixson theory, and the construction of stable manifolds, as well as an introduction to geodesic flows and the study of hyperbolicity (the latter is often absent in a first introduction). Moreover, the authors introduce the basics of symbolic dynamics, the construction of symbolic codings, invariant measures, Poincaré's recurrence theorem and Birkhoff's ergodic theorem.

The exposition is mathematically rigorous, concise and direct: all statements (except for some results from other areas) are proven. At the same time, the text illustrates the theory with many examples and 140 exercises of variable levels of difficulty. The only prerequisites are a background in linear algebra, analysis and elementary topology.

This is a textbook primarily designed for a one-semester or two-semesters course at the advanced undergraduate or beginning graduate levels. It can also be used for self-study and as a starting point for more advanced topics.

Keywords

Ergodic Theory Hyperbolic Dynamics Low-Dimensional Dynamics Symbolic Dynamics Topological Dynamics

Authors and affiliations

  • Luis Barreira
    • 1
  • Claudia Valls
    • 2
  1. 1.Departamento de MatemáticaInstituto Superior TécnicoLisbonPortugal
  2. 2.Departamento de MatemáticaInstituto Superior TécnicoLisbonPortugal

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-4835-7
  • Copyright Information Springer-Verlag London 2013
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-4834-0
  • Online ISBN 978-1-4471-4835-7
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book
Industry Sectors
Aerospace