Equivariant Unfolding Theory
Unfolding theory is the study of parametrized families of perturbations of a given germ. In the symmetric setting, when a group Γis acting, we consider only Γ-equivalent perturbations. There is a general theory of Γ-unfoldings, analogous to unfoldings in the nonsymmetric case (Volume I, Chapter III). The heart of the singularity theory approach to bifurcations with symmetry is the equivariant unfolding theorem, which asserts that every Γ-equivariant mapping with finite Γ-codimension has a universal Γ-unfolding and gives a computable test for universality.
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