Bifurcations of piecewise smooth vector fields via geometric singular perturbations

Abstract

We deal with piecewise smooth vector fields on the plane and 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 piecewise smooth vector fields presenting typical
singularities and singularly perturbed smooth systems.