Singularity Theory and its Applications: Warwick 1989, Part II: Singularities, Bifurcations and Dynamics

P. J. Aston (auth.), Mark Roberts, Ian Stewart (eds.)9780387537368, 0387537368

A workshop on Singularities, Bifuraction and Dynamics was held at Warwick in July 1989, as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory and applications in the sciences. The papers are original research, stimulated by the symposium and workshop: All have been refereed and none will appear elsewhere. The main topic of volume II is new methods for the study of bifurcations in nonlinear dynamical systems, and applications of these.

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Table of contents :
Scaling Laws and Bifurcation….Pages 1-21
Bifurcation from a manifold….Pages 22-37
Structurally stable heteroclinic cycles in a system with O(3) symmetry….Pages 38-62
Boundary conditions as symmetry constraints….Pages 63-79
Equivariant bifurcations and morsifications for finite groups….Pages 80-106
On a codimension-four bifurcation occurring in optical bistability….Pages 107-121
The center manifold for delay equations in the light of suns and stars….Pages 122-141
Local structure of equivariant dynamics….Pages 142-166
On the bifurcations of subharmonics in reversible systems….Pages 167-192
Classification of symmetric caustics I: symplectic equivalence….Pages 193-219
Symplectic singularities and optical diffraction….Pages 220-255
Dynamics near steady state bifurcations in problems with spherical symmetry….Pages 256-265
Caustics in time reversible hamiltonian systems….Pages 266-277
Some complex differential equations arising in telecommunications….Pages 278-293
Classification of two-parameter bifurcations….Pages 294-300
Versal deformations of infinitesimally symplectic transformations with antisymplectic involutions….Pages 301-320