Análise global de sistemas quadráticos e cúbicos com duas circunferências não-concêntricas invariantes - Reinol, Alisson de Carvalho [UNESP] (2014)
In this work, we perform a global study of quadratic and cubic planar polynomial differential systems having two nonconcentric circles as invariant algebraic curves. We give all possible global phase portraits on the Poincar´e disk of the polynomial vector fields associated to these systems. We show that there exist 3 topological equivalent classes for quadratic cases and 19 topological equivalent classes for cubic ones. As a consequence, we prove that these polynomial differential systems have no limit cycles.