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

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.

Scaling Laws and Bifurcation.- Bifurcation from a manifold.- Structurally stable heteroclinic cycles in a system with O(3) symmetry.- Boundary conditions as symmetry constraints.- Equivariant bifurcations and morsifications for finite groups.- On a codimension-four bifurcation occurring in optical bistability.- The center manifold for delay equations in the light of suns and stars.- Local structure of equivariant dynamics.- On the bifurcations of subharmonics in reversible systems.- Classification of symmetric caustics I: symplectic equivalence.- Symplectic singularities and optical diffraction.- Dynamics near steady state bifurcations in problems with spherical symmetry.- Caustics in time reversible hamiltonian systems.- Some complex differential equations arising in telecommunications.- Classification of two-parameter bifurcations.- Versal deformations of infinitesimally symplectic transformations with antisymplectic involutions.