Dynamical Systems by Example

  • Luís Barreira
  • Claudia Valls

Part of the Problem Books in Mathematics book series (PBM)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Theory and Problems

    1. Front Matter
      Pages 1-1
    2. Luís Barreira, Claudia Valls
      Pages 3-14
    3. Luís Barreira, Claudia Valls
      Pages 15-22
    4. Luís Barreira, Claudia Valls
      Pages 23-33
    5. Luís Barreira, Claudia Valls
      Pages 35-47
    6. Luís Barreira, Claudia Valls
      Pages 49-56
    7. Luís Barreira, Claudia Valls
      Pages 57-67
  3. Problems and Solutions

    1. Front Matter
      Pages 69-69
    2. Luís Barreira, Claudia Valls
      Pages 71-93
    3. Luís Barreira, Claudia Valls
      Pages 95-114
    4. Luís Barreira, Claudia Valls
      Pages 115-134
    5. Luís Barreira, Claudia Valls
      Pages 135-167
    6. Luís Barreira, Claudia Valls
      Pages 169-188
    7. Luís Barreira, Claudia Valls
      Pages 189-215
  4. Back Matter
    Pages 217-223

About this book


This book comprises an impressive collection of problems that cover a variety of carefully selected topics on the core of the theory of dynamical systems. Aimed at the graduate/upper undergraduate level, the emphasis is on dynamical systems with discrete time. In addition to the basic theory, the topics include topological, low-dimensional, hyperbolic and symbolic dynamics, as well as basic ergodic theory. As in other areas of mathematics, one can gain the first working knowledge of a topic by solving selected problems. It is rare to find large collections of problems in an advanced field of study much less to discover accompanying detailed solutions. This text fills a gap and can be used as a strong companion to an analogous dynamical systems textbook such as the authors’ own Dynamical Systems (Universitext, Springer) or another text designed for a one- or two-semester advanced undergraduate/graduate course. The book is also intended for independent study.

Problems often begin with specific cases and then move on to general results, following a natural path of learning. They are also well-graded in terms of increasing the challenge to the reader. Anyone who works through the theory and problems in Part I will have acquired the background and techniques needed to do advanced studies in this area. Part II includes complete solutions to every problem given in Part I with each conveniently restated. Beyond basic prerequisites from linear algebra, differential and integral calculus, and complex analysis and topology, in each chapter the authors recall the notions and results (without proofs) that are necessary to treat the challenges set for that chapter, thus making the text self-contained.


problems dynamical systems exercises dynamical systems dynamical systems topological dynamics low-dimensional dynamics hyperbolic dynamics symbolic dynamics ergodic theory basic theory dynamical systems supplement text dynamical systems homework problems dynamical systems

Authors and affiliations

  • Luís Barreira
    • 1
  • Claudia Valls
    • 2
  1. 1.Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal
  2. 2.Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-15914-6
  • Online ISBN 978-3-030-15915-3
  • Series Print ISSN 0941-3502
  • Series Online ISSN 2197-8506
  • Buy this book on publisher's site