We will describe some qualitative and geometricaspects of non-smooth dynamical systems theory around typical singularities. We will establish a interaction between non-smooth systems and the geometric singular perturbation theory. Such systems are represented by discontinuous vector fields where its discontinuity set is a codimension one algebraic variety. By means of a regularization process proceeded by a blow-up technique we are able to bring out some results that bridge the space between discontinuous systems and singularly perturbed smooth systems.
News published in Agência FAPESP Newsletter about the scholarship: