Structures in Dynamics

Finite Dimensional Deterministic Studies


  • H.W. Broer, University of Groningen, Groningen, The Netherlands
  • F. Dumortier, Limburgs Universitair Centrum, Belgium
  • S.J. van Strien, Delft University, Delft, The Netherlands
  • F. Takens, University of Groningen, Groningen, The Netherlands

The study of non-linear dynamical systems nowadays is an intricate mixture of analysis, geometry, algebra and measure theory and this book takes all aspects into account.Presenting the contents of its authors' graduate courses in non-linear dynamical systems, this volume aims at researchers who wish to be acquainted with the more theoretical and fundamental subjects in non-linear dynamics and is designed to link the popular literature with research papers and monographs.All of the subjects covered in this book are extensively dealt with and presented in a pedagogic form. These include the presentation of an environment for the route to chaos by quasi-periodicity (which is related to the Landau-Lifschitz and Ruelle-Takens scenario's concerning the onset of turbulence); the theories of 1-dimensional dynamics, singularities in planar vector fields, and quasi-periodicity in dissipative systems.
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Book information

  • Published: November 1991
  • Imprint: NORTH-HOLLAND
  • ISBN: 978-0-444-89257-7


This is a good and instructive book about non-linear dynamics.
Australian and New Zealand Physicist

Table of Contents

Preface. 1. Introduction to dynamical systems (H.W. Broer). 2. Genericity and structural stability (H.W. Broer and F. Dumortier). 3. Bifurcations (F. Takens). 4. A family of quasi-periodic attractors (H.W. Broer). 5. Chaos (F. Takens). 6. Interval maps (S.J. v. Strien). 7. Local study of planar vector fields: singularities and their unfoldings (F. Dumortier). 8. The thermodynamic formalism (F. Takens). 9. Conservative dynamical systems (H.W. Broer). Subject index.