Sistemas lento-rápido por partes e aplicações

Abstract

This dissertation presents a study of piecewise-smooth (or discontinuous) vector fields, with an emphasis on the Filippov’s convention and the Sotomayor-Teixeira’s regulariza tion process. We also pay special attention to slow-fast systems, which are a class of 1- parameter smooth vector fields defined on more than one time scale and which establish relations with discontinuous vector fields. Initially, results and definitions are presented from the classical theory of smooth vector fields. The aim is to establish a natural con nection between the set of smooth vector fields and the set of discontinuous vector fields. Then we present the main concepts and results associated with slow-fast systems and piecewise-smooth systems. Finally, a piecewise-smooth vector field model applied to the study of climate dynamics is presented and discussed.