Evaluation of a Germ Stability of a Differentiable Mapping Defined by a Mathematical Model

Abstract

The paper presents a set of algorithms to assess: the set of singular points of a differentiable mapping defined by some mathematical model; the stability of the germ of this mapping in its singular point, and (in the case of its stability) the form of such a germ in cases of corank 1 and all the possible relations of dimensions of the domain and mapping image. The stability of these germs in all singular points of the mapping under study is a necessary condition for the stability of the mapping in its domain. The implementation of the developed algorithms can be used to verify the model under study by investigating mappings defined by it.