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Nonlinear Dynamical Systems and Chaos

  • Conference proceedings
  • © 1996

Overview

Editors:
  1. H. W. Broer

    1. Institute of Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands

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  2. S. A. Gils

    1. Faculty of Mathematics and Computer Science, University of Twente, Enschede, The Netherlands

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  3. I. Hoveijn

    1. Institute of Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands

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  4. F. Takens

    1. Institute of Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands

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  • The book can be recommended to researchers specializing in dynamical systems." - Applied Mathematics, XL

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 19)

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Table of contents (21 papers)

  1. Front Matter

    Pages i-vii
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  2. Symmetries in dynamical systems

    1. Symplecticity, reversibility and elliptic operators

      • Thomas J. Bridges
      Pages 1-20

    2. The Rolling Disc

      • R. Cushman, J. Hermans, D. Kemppainen
      Pages 21-60

    3. Testing for S n -Symmetry with a Recursive Detective

      • Karin Gatermann
      Pages 61-78

    4. Normal forms of vector fields satisfying certain geometric conditions

      • I. U. Bronstein, A. Ya. Kopanskii
      Pages 79-101

    5. On symmetric ω-limit sets in reversible flows

      • Jeroen S. W. Lamb, Matthew Nicol
      Pages 103-120

    6. Symmetry Breaking in Dynamical Systems

      • Reiner Lauterbach
      Pages 121-143

    7. Invariant C j functions and center manifold reduction

      • Matthias Rumberger, JĂĽrgen Scheurle
      Pages 145-153

    8. Hopf bifurcation at k-fold resonances in conservative systems

      • JĂĽrgen Knobloch, AndrĂ© Vanderbauwhede
      Pages 155-170

  3. KAM theory and other perturbation theories

    1. Families of Quasi-Periodic Motions in Dynamical Systems Depending on Parameters

      • H. W. Broer, G. B. Huitema, M. B. Sevryuk
      Pages 171-211

    2. Towards a Global Theory of Singularly Perturbed Dynamical Systems

      • John Guckenheimer
      Pages 213-225

    3. Equivariant Perturbations of the Euler Top

      • Heinz HanĂźmann
      Pages 227-252

    4. On stability loss delay for a periodic trajectory

      • A. I. Neishtadt, C. SimĂł, D. V. Treschev
      Pages 253-278

    5. Parametric and autoparametric resonance

      • M. Ruijgrok, F. Verhulst
      Pages 279-298

    6. Global attractors and bifurcations

      • Marcelo Viana
      Pages 299-324

  5. Time series analysis

    1. Estimation of dimension and order of time series

      • Floris Takens
      Pages 405-422
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Keywords

About this book

Symmetries in dynamical systems, "KAM theory and other perturbation theories", "Infinite dimensional systems", "Time series analysis" and "Numerical continuation and bifurcation analysis" were the main topics of the December 1995 Dynamical Systems Conference held in Groningen in honour of Johann Bernoulli. They now form the core of this work which seeks to present the state of the art in various branches of the theory of dynamical systems. A number of articles have a survey character whereas others deal with recent results in current research. It contains interesting material for all members of the dynamical systems community, ranging from geometric and analytic aspects from a mathematical point of view to applications in various sciences.

Editors and Affiliations

  • Institute of Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands

    H. W. Broer, I. Hoveijn, F. Takens

  • Faculty of Mathematics and Computer Science, University of Twente, Enschede, The Netherlands

    S. A. Gils

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