Generic behavior of a piecewise smooth vector field with non-smooth   switching surface
  This paper consists in discussing some issues on generic local classification of typical singularities of $2D$ piecewise smooth vector fields when the switching set is an algebraic variety. The main focus is to obtain classification results concerning structural stability and generic codimension one bifurcations. 
Juliana Larrosa, Marco A. Teixeira, Tere M-Seara
math.DS