Dynamical systems with multiple time scales

Abstract

In this project we deal with singularly perturbed systems of ordinary differential equations expressed by (n-1)--parameter families of vector fields. The inherent characteristic of such systems is the presence of a number n of time scales. Recently, we extend Fenichel theory for such systems. Now, we intend to continue investigating other important aspects that are part of Geometric Singular Perturbation Theory in the context of systems with n time scales. In addition, we also consider singularly perturbed systems with symmetries. From the point of view of Fenichel theory, our main question is to know how the dynamics properties of symmetry are affected by singular perturbations. Finally, the study on limit cycles in singularly perturbed Liénard systems will also be considered. (AU)