Geometric theory of the singularly perturbed differential equations

Abstract

In this project the main goal is to study systems of singularly perturbed ordinary differential equations involving multiple different time scales. The study will encompass both the case where the vector field associated to such systems is smooth, as well as the case where the field vector is non-smooth (Filippov kind). The main feature of such systems is the possibility of working at different time scales. We intend to develop a mathematical theory in order to study these systems. The main goal is to build a theory, inspired by the Geometric Singular Perturbation Theory, for systems involving n different time scales, where n is greater than 2. (AU)