Path formulation for multiparameter D3-equivariant bifurcation problems - Furter, Jacques-Élie; Sitta, Angela Maria [UNESP] (Cellule MathDoc/Centre Mersenne, 2010)
We implement a singularity theory approach, the path formulation, to classify D3-equivariant bifurcation problems of corank 2, with one or two distinguished parameters, and their perturbations. The bifurcation diagrams are identified with sections over paths in the parameter space of a Ba-miniversal unfolding f0 of their cores. Equivalence between paths is given by diffeomorphisms liftable over the projection from the zero-set of F0 onto its unfolding parameter space. We apply our results to degenerate bifurcation of period-3 subharmonics in reversible systems, in particular in the 1:1-resonance.
Keywords: 1:1-resonance; Degenerate bifurcation; Equivariant bifurcation; Path formulation; Reversible systems; Singularity theory; Subharmonic bifurcation