Finite $C^0$-determinacy of real analytic map germs with isolated instability

Abstract

Let f : (R n , 0) → (R p , 0) be a real analytic map germ with isolated instability. We prove that if n = 2 and p = 2, 3, then f is finitely C 0-determined. This result can be seen as a weaker real counterpart of Mather-Gaffney finite determinacy criterion.