Poincare index and periodic solutions of perturbed autonomous systems

Abstract

The basic tool of classical results by Malkin and Melnikov on bifurcation of periodic solutions from nondegenerate cycles of autonomous systems with periodic perturbations is an implicit function theorem. In this paper the Poincare index is used to avoid the requirement of nondegeneracity for the unperturbed cycles and to provide additional geometrical properties of periodic solutions of the perturbed system.