Nonlinear Dynamical Systems and Chaos

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, Jürgen Scheurle

      Pages 145-153

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

      • Jürgen Knobloch, André 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 Hanßmann

      Pages 227-252

   4. On stability loss delay for a periodic trajectory

      • A. I. Neishtadt, C. Simó, 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

4. Infinite dimensional systems

   1. Modulated waves in a perturbed Korteweg-de Vries equation

      • Stephan A. van Gils, Edy Soewono

      Pages 325-346

   2. Hamiltonian Perturbation Theory for Concentrated Structures in Inhomogeneous Media

      • E. R. Fledderus, E. van Groesen

      Pages 347-372

   3. On instability of minimal foliations for a variational problem on T ²

      • Xianhua Huang

      Pages 373-383

   4. Local and Global Existence of Multiple Waves Near Formal Approximations

      • Xiao-Biao Lin

      Pages 385-404

5. Time series analysis

   1. Estimation of dimension and order of time series

      • Floris Takens

      Pages 405-422

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.

• KAM theory
• bifurcation
• chaos
• dynamical systems
• time series analysis

• 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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