Deformations of real singularities (Q2277617)

The author considers the problem to determine what other singularities, or constellations of singularities, occur in the deformation of a given one. There is a well-known method to construct a versal deformation of a given isolated singularity of a function. But this formula is not well adapted to the solution of the above problem. In the cases of simple singularities, simple-elliptic singularities and cusp singularities, there are particular constructions of miniversal deformations on the complex number field. The author investigates what leads to the real case. There are three main parts: on simple singularities, on simple- elliptic singularities and on cusp singularities. Each of these is divided into two chapters: the complex case, then the real case. But its algorithms to list the singularities occurring in the deformation is not presented here by the reason of space.