Sistemas descontínuos lento-rápidos e aplicações

Abstract

In this work we study dynamical systems focused on two areas: discontinuous systems and singular perturbation problems. We analyze the intersection of these two areas through some theoretical results. In the first moment, we will present a theory similar to Fenichel's Theory for singularly perturbed discontinuous systems, later we will show that a system obtained via regularization can be associated with a singular perturbation problem. In addition, we will study a mathematical modeling in the area of climatology, with the objective of analyzing the bifurcations of singularities and the existence of a periodic orbit for certain specific parameters. In this model, we cannot apply Fenichel's theory, for this reason we use an ad-hoc application of Fenichel's Theory to demonstrate the desired results. Finally, we will present some unpublished results for the climatological model.