Asbract

We will present some results for the understanding of the dynamics of non-smooth systems. In this work our aim is to study the dynamics of a discontinuous system when its discontinuity set belongs to a general class of algebraic sets. Our approach combines several techniques such as regularization process, blowing-up method and singularperturbation theory. Some of the results generalize the regularization process introduced by Sotomayor and Teixeira. This is a joint work with Marco A. Teixeira and Paulo R. da Silva.