Stability of unfoldings in the context of equivariant contact- equivalence (Q1105248)

The notion of equivariant contact-equivalence between germs of \(C^{(\infty)}\) equivariant mappings, introduced by M. Golubitsky and D. Schaeffer, is useful to study perturbed bifurcation problems having a certain symmetry property. The ``unfolding theorem'' for qualitative description of the symmetry-preserving perturbations of these problems plays an important role in the study. A relevant notion is that of stability of unfoldings. In this paper, the author proves the equivalence of the universality and the stability of unfoldings in the context of equivariant contact-equivalence.