Non-generic cusps

M. Misiurewicz and A. Rodrigues

Abstract

We find the order of contact of the boundaries of the cusp for two-parameter families of vector fields on the real line or diffeomorphisms of the real line, for cusp bifurcations of codimensions 1 and 2. Moreover, we create a machinery that can be used for the same problem in higher codimensions and perhaps for other, similar problems.