In this paper we shall prove that two basic theorems of singularity theory, the versatility theorem and the finite determinacy theorem, are valid for a large class of equivalence relations on germs of mappings.
An integral formula for the subregular germ of a [italic small capital]K-orbital integral is developed. The formula holds for any reductive group over a [italic]p-adic field of characteristic zero. This expression of the subregular germ is obtained by applying Igusa's theory of …
These notes give a fairly elementary introduction to the local theory of differentiable mappings. Sard's Theorem and the Preparation Theorem of Malgrange and Mather are the basic tools and these are proved first. There follows a number of illustrations including: the local part …