Estudo qualitativo de campos suaves por partes via problema de perturbação singular

Abstract

In this work we will show that, given a piecewise smooth vector field, we can apply the regularization method and, from it, via blow-up, turn it into a singular perturbation problem. By doing that, we can use the tools from singular perturbation theory to perform a qualitative study of piecewise smooth vector fields. Finally, we will show that, through successive changes of coordinates, a singularity of a discontinuous submanifold of codimension k, where k=1 or k=2, can be transformed into a singularity of codimension 0 in order to study the qualitative behavior in this submanifold, where the Filippov’s convention holds.