Medium amplitude limit cycles in second order perturbed polynomial Liénard systems

Abstract

We consider polynomial generalized Liénard systems that come from second order polynomial perturbations of a linear center. For these systems we found a generic (open and dense) subset in the space of perturbations of degree 2 l , with l ≥ 1 , such that each associated perturbed generalized Liénard system has at most 2 l − 1 medium limit cycles. Moreover, we show that this upper bound is reached. In addition, some concrete examples are given.