Abstract

We deal with nonlinear periodic differential systems depending on a small parameter. The unperturbed system has an invariant manifold of periodic solutions. We provide sufficient conditions in order that some of these periodic orbits persist after the perturbation. The key tool for proving the main result is the Lyapunov-Schmidt reduction method applied to the Poincaré-Andronov mapping.

This is a joint work with J.P. Françoise and J. Llibre