Two-parameter families of implicit differential equations.

Abstract

We study in this paper local codimension 2 singularities of (first order) implicit differential equations F(x, y, p) = 0, where F is a germ of a smooth function, p = dy dx , Fp = 0 and Fpp = 0 at the singular point. We obtain topological models of these singularities and deal with their bifurcations in generic 2-parameter families of equations.