Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3

Abstract

A cusp type germ of vector fields is a C∞ germ at 0[omitted formula]2, whose 2-jet is C∞ conjugate to [omitted formula] We define a submanifold of codimension 5 in the space of germs [omitted formula] consisting of germs of cusp type whose 4-jet is C0 equivalent to [omitted formula] Our main result can be stated as follows: any local 3-parameter family in (0, 0) [omitted formula]2[omitted formula]3 cutting [omitted formula]. © 1987, Cambridge University Press. All rights reserved.