On Sliding Periodic Solutions for Piecewise Continuous Systems Defined on the 2-Cylinder

This paper deals with discontinuous differential equations defined on the 2--dimensional cylinder. The main goal is to exhibit conditions for the existence of typical periodic solutions of such systems. An averaging method for computing sliding periodic solutions is developed, subject to convenient assumptions. We also apply the method to example problems. The main tools used are structural stability theory for discontinuous differential systems and Brouwer degree theory.