The Analytic Classification of Plane Curves with Two Branches
  In this paper we solve the problem of analytic classification of plane curves singularities with two branches by presenting their normal forms. This is accomplished by means of a new analytic invariant that relates vectors in the tangent space to the orbits under analytic equivalence in a given equisingularity class to K\"ahler differentials on the curve. 
Abramo Hefez, Marcelo Escudeiro Hernandes and Maria Elenice Rodrigues   Hernandes
math.AG