Upper Bounds for Limit Cycles from Isochronous Centers
by
Bourama Toni
Lane College, Jackson, Tennessee, 38301

We investigate the higher order upper bounds to the number of limit cycles from isochronous centers in the direction of a polynomial 1-form perturbation. These upper bounds are explicitly computed for a polynomial preserving linearizing transformation using a method based on the relative cohomology decomposition of polynomial 1-forms along with a step reduction process. As an application we analyze perturbations of the linear 1-form, and of a Darboux linearizable cubic Hamiltonian center.

Date received: February 27, 2003