Um estudo sobre centros globais em sistemas planares

Abstract

In this dissertation, rstly, we show that a polynomial di erential system of even order does not have a global center. Next, we characterize all Liénard polynomial systems having a global center at the origin. In particular, we provide an explicit expression of all Liénard polynomial systems of degree three with a global center at the origin. Finally, we classify all degree three and degree ve Kukles systems with a global center at the origin.