Bifurcations of Non Smooth Vector Fields on ${\mathbb{R}}^2$ by Geometric Singular Perturbations

Our object of study is non smooth vector fields on ${\mathbb{R}}^2$. We apply the techniques of geometric singular perturbations in non smooth vector fields after regularization and a blow$-$up. In this way 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.