Milnor fibrations and regularity conditions for real analytic mappings

Abstract

When f : R power n to R power p, is a surjective real analytic map with isolated critical value, we prove that the (m)-regularity condition (in a sense we define) ensures that f ||f|| is a fibration on small spheres, f induces a fibration on the tubes and both fibrations are equivalent. In particular, we make the statement of [12] more precise in the case of isolated critical point and we extend it to the case of an isolated critical value.