Nonlinear Dynamical Systems and Chaos

✍ Scribed by Thomas J. Bridges (auth.), H. W. Broer, S. A. van Gils, I. Hoveijn, F. Takens (eds.)

• Publisher: Birkhäuser Basel
• Year: 1996
• Tongue: English
• Leaves: 464
• Series: Progress in Nonlinear Differential Equations and Their Applications 19
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-vii
Symplecticity, reversibility and elliptic operators....Pages 1-20
The Rolling Disc....Pages 21-60
Testing for S n -Symmetry with a Recursive Detective....Pages 61-78
Normal forms of vector fields satisfying certain geometric conditions....Pages 79-101
On symmetric ω -limit sets in reversible flows....Pages 103-120
Symmetry Breaking in Dynamical Systems....Pages 121-143
Invariant C j functions and center manifold reduction....Pages 145-153
Hopf bifurcation at k-fold resonances in conservative systems....Pages 155-170
Families of Quasi-Periodic Motions in Dynamical Systems Depending on Parameters....Pages 171-211
Towards a Global Theory of Singularly Perturbed Dynamical Systems....Pages 213-225
Equivariant Perturbations of the Euler Top....Pages 227-252
On stability loss delay for a periodic trajectory....Pages 253-278
Parametric and autoparametric resonance....Pages 279-298
Global attractors and bifurcations....Pages 299-324
Modulated waves in a perturbed Korteweg-de Vries equation....Pages 325-346
Hamiltonian Perturbation Theory for Concentrated Structures in Inhomogeneous Media....Pages 347-372
On instability of minimal foliations for a variational problem on T 2 ....Pages 373-383
Local and Global Existence of Multiple Waves Near Formal Approximations....Pages 385-404
Estimation of dimension and order of time series....Pages 405-422
On the computation of normally hyperbolic invariant manifolds....Pages 423-447
The Computation of Unstable Manifolds Using Subdivision and Continuation....Pages 449-459
Back Matter....Pages 460-463

✦ Subjects

Analysis; Manifolds and Cell Complexes (incl. Diff.Topology); Numerical Analysis