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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...

Projections of surfaces with singular boundary

Hassan Babiker (2008)

Banach Center Publications

Singular projections of generic 2-dim surfaces in ℝ³ with singular boundary to 2-space are studied. The case of projections of surfaces with nonsingular boundary has been treated by Bruce and Giblin. The aim of this paper is to generalise these results to the simplest singular case where the boundary of the surface consists of two transversally intersecting lines. Local models for germs of generic singular projections of corank ≤ 1 and codimension ≤ 3 are given. We also present geometrical realisations...

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