Generic Bifurcations of Planar Filippov Systems via Geometric Singular Perturbations

Abstract

In this paper we deal with non$-$smooth vector fields on the plane. We prove that the analysis of their local behavior around certain typical singularities can be treated via singular perturbation theory. In fact, after a regularization of a such system and a blow$-$up we are able to bring out some results that bridge the space between non$-$smooth dynamical systems presenting typical singularities and singularly perturbed smooth systems.