Dynamics, Bifurcation and Symmetry New Trends and New Tools

This book collects contributions to the conference" Dynamics, Bifurcation and Symmetry, new trends and new tools", which was held at the Institut d'Etudes Sci­ entifiques de Cargese (France), September 3-9, 1993. The first aim of this conference was to gather and summarize the work of the European Bifurcation Theory Group after two years of existence (the EBTG links european laboratories in five countries via an EC grant). Thanks to a NATO ARW grant, the conference developed into an international meeting on bifurcation theory and dynamical systems, with the partic­ ipation of leading specialists not only from Europe but also from overseas countries (Canada, USA, South America). It was a great satisfaction to notice the active, and quite enthusiastic participation of many young scientists. This is reflected in the present book for which many contributors are PhD students or post-doc researchers. Although several "big" themes (bifurcation with symmetry, low dimensional dynam­ ics, dynamics in EDP's, applications, . . . ) are present in these proceedings, we have divided the book into corresponding parts. In fact these themes overlap in most contributions, which seems to reflect a general tendancy in nonlinear science. I am very pleased to thank for their support the NATO International Exchange Scientific Program as well as the EEC Science Program, which made possible the suc­ cess of this conference.

A spatial center manifold approach to a hydrodynamical problem with O(2) symmetry.- Analysing bifurcations in the Kolmogorov flow equations.- Oscillator networks with the symmetry of the unit quaternion group.- An investigation of a mode interaction involving period-doubling and symmetry-breaking bifurcations.- Sets, lines and adding machines.- Mixed-mode solutions in mode interaction problems with symmetry.- A classification of 2-modes interactions with SO(3) symmetry and applications.- Non linear parabolic evolutions in unbounded domains.- Eigenvalue, movement for a class of reversible Hamiltonian systems with three degrees of freedom.- Blowing-up in equivariant bifurcation theory.- A remark on the detection of symmetry of attractors.- Coupled cells: wreath products and direct products.- Hopf bifurcations on generalized rectangles with Neumann boundary conditions.- The role of geometry in computational dynamics.- Hopf bifurcation at k-fold resonances in equivariant reversible systems.- Symmetries and reversing symmetries in kicked systems.- Exclusion of relative equilibria.- Bifurcation of periodic orbits in 1:2 resonance: a singularity theory approach.- Hamiltonian structure of the reversible nonsemisimple 1:1 resonance.- Instantaneous symmetry and symmetry on average in the Couette-Taylor and Faraday experiments.- The path formulation of bifurcation theory.- Codimension two local analysis of spherical Bénard convection.- A geometric Hamiltonian approach to the affine rigid body.- A note on discontinuous vector fields and reversible mappings.- Bifurcation of singularities near reversible systems.- On a new phenomenon in bifurcations of periodic orbits.- An inhomogeneous Picard-Fuchs equation.- Hopf bifurcation in symmetrically coupled lasers.