On nonsmooth perturbations of nondegenerate planar centers

Agraïments: Supported by a FAPESP-BRAZIL grant 2012/10231-7.We provide sufficient conditions for the existence of limit cycles of non-smooth perturbed planar centers, when the set of discontinuity is an algebraic variety. It is introduced a mechanism which allows us to deal with such system, even in higher dimension. The main tool used in this paper is the averaging method. Two applications are given in careful detail