LIMIT CYCLES OF THE DISCONTINUOUS PIECEWISE DIFFERENTIAL SYSTEMS ON THE CYLINDER^∗

In order to understand the dynamics of the differential systems the limit cycles play a main role, but in general their study is not easy. These last years an increasing interest appeared for studying the limit cycles of some classes of discontinuous piecewise differential systems, due to the rich applications of this kind of differential systems. Very few papers studied the limit cycles of the discontinuous piecewise differential systems in spaces different from the plane R². Here we study the limit cycles of a class of discontinuous piecewise differential systems on the cylinder.