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Structures in Dynamics

Finite Dimensional Deterministic Studies

  • 1st Edition, Volume 2 - November 5, 1991
  • Latest edition
  • Authors: H.W. Broer, F. Dumortier, S.J. van Strien, F. Takens
  • Language: English

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… Read more

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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

  • Edition: 1
  • Latest edition
  • Volume: 2
  • Published: November 5, 1991
  • Language: English

About the authors

HB

H.W. Broer

Affiliations and expertise
University of Groningen, Groningen, The Netherlands

FD

F. Dumortier

Affiliations and expertise
Limburgs Universitair Centrum, Belgium

Sv

S.J. van Strien

Affiliations and expertise
Delft University, Delft, The Netherlands

FT

F. Takens

Affiliations and expertise
University of Groningen, Groningen, The Netherlands

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