Versal deformations

Abstract

Ordinarily in the consideration of all possible singularities the principal interest focusses on the generic case, since all the more complicated singularities may be got rid of by a small perturbation. For example, a generic function has only nondegenerate critical points; degenerate critical points, like the critical point of the function x³, decompose into nondegenerate ones under a suitable small deformation, for example x³ − εx.