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Path formulation for multiparameter $𝔻_{3}$ -equivariant bifurcation problems

Jacques-Élie Furter; Angela Maria Sitta — 2010

Annales de l’institut Fourier

We implement a singularity theory approach, the path formulation, to classify $𝔻_{3}$ -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 $𝔻_{3}$ -miniversal unfolding $F_{0}$ of their cores. Equivalence between paths is given by diffeomorphisms liftable over the projection from the zero-set of $F_{0}$ onto its unfolding parameter space. We apply our results to degenerate...

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Path formulation for multiparameter 𝔻 3 -equivariant bifurcation problems

Path formulation for multiparameter $𝔻_{3}$ -equivariant bifurcation problems