Poincare index and periodic solutions of perturbed autonomous systems

Details Poincare index and periodic solutions of perturbed autonomous systems Poincare index and periodic solutions of perturbed autonomous systems

2007-09-28

arxiv.org/abs/0710.0006v1

Mathematics

Classical Analysis and ODEs

To appear in Trans. Mosc. Math. Soc

Scientific paper

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.

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