Invariant sets for piecewise smooth differential equations defined on two dimensional compact manifolds

Abstract

In this project, we will study families of piecewise smooth differential equations defined on compact two-dimensional manifolds $M$. Our main objective is to exhibit conditions for a piecewise polynomial system defined in $M$ to admit periodic orbits in cases where $M$ is the sphere or the torus. We will also study the structural stability in the case of piecewise smooth differential equations defined in a $M$ polyhedron, considering the possibilities for the sliding dynamics on the edges. (AU)