Abstract

The study of planar perturbed Hamiltonian systems is a classic idea. One of the simplest planar Hamiltonian systems is the linear center. Special polynomial perturbations of this Hamiltonian system give polynomial planar systems of Liénard type. Some limit cycles of such systems are generated, under the perturbation, from cycles of the linear center. We will give an upper bound of the number of these limit cycles. Such upper bound depends only on the degree of the perturbation.