Topological equivalence of finitely determined real analytic plane-to-plane map germs

Abstract

Generic smooth map germs $({\mathsf R}^2,0)\to ({\mathsf R}^2,0)$ are topologically equivalent to cones of mappings $S^1\to S^1$. We carry out a complete topological classification of smooth stable mappings of the circle and show how this classification leads, via the result mentioned above, to a topological classification of finitely determined real analytic map germs $({\mathsf R}^2,0)\to ({\mathsf R}^2,0)$.