Structures in Dynamics

Structures in Dynamics

Finite Dimensional Deterministic Studies

1st Edition - November 5, 1991

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  • Authors: H.W. Broer, F. Dumortier, S.J. van Strien, F. Takens
  • eBook ISBN: 9780444596253

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Description

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.

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.

Product details

  • No. of pages: 322
  • Language: English
  • Copyright: © North Holland 1991
  • Published: November 5, 1991
  • Imprint: North Holland
  • eBook ISBN: 9780444596253

About the Authors

H.W. Broer

Affiliations and Expertise

University of Groningen, Groningen, The Netherlands

F. Dumortier

Affiliations and Expertise

Limburgs Universitair Centrum, Belgium

S.J. van Strien

Affiliations and Expertise

Delft University, Delft, The Netherlands

F. Takens

Affiliations and Expertise

University of Groningen, Groningen, The Netherlands

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