GOURSAT SYSTEMS WITH SINGULARITIES OF DIFFERENT ORDERS IN ONE DIMENSION OF ITS SMALL GROWTH VECTOR

We study rank-2 distributions satisfying the so-called Goursat conditions (GC) [2,3] and provide local forms in $\mathbb{R}^n$ for a family of distributions that satisfy (GC) everywhere and have a singularity of order $k$ and dimension one in the small growth vector [3,10]. However, for each singularity, we obtain a new non-equivalent local form. This singularity can be of order $k=2,3,4, \ldots, n-3$.