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∈ℝ 2 , whose 2-jet is C ∞ conjugate to We define a submanifold of codimension 5 in the space of germs consisting of germs of cusp type whose 4-jet is C 0 equivalent to Our main result can be stated as follows: any local 3-parameter family in (0, 0) ∈ ℝ 2 × ℝ 3 cutting transversally in (0, 0) is fibre- C 0 equivalent to