Abstract. We study the maximum number of limit cycles that bifurcate from the periodic solutions of the family of isochronous cubic polynomial centerṡwhen it is perturbed inside the classes of all continuous and discontinuous cubic polynomial differential systems. We obtain that the maximum number of limit cycles which can be obtained by the averaging method of first order is 3 for the perturbed continuous systems and for the perturbed discontinuous systems at least 12 limit cycles can appear.

No abstract

Abstract. We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of cubic polynomial differential centers when it is perturbed inside the class of all cubic polynomial differential systems. The family considered is the unique family of weight-homogeneous polynomial differential systems of weight-degree 2 with a center.