On the behavior of periodic solutions of planar autonomous hamiltonian systems with multivalued periodic perturbation

摘要

Aim of the paper is to provide a method to analyze the behavior of T- periodic solutions x~ε, ε > 0, of a perturbed planar Hamiltonian system near a cycle x0, of smallest period T, of the unperturbed system. The perturbation is represented by a T-periodic multivalued map which vanishes as ε > 0. In several problems from nonsmooth mechanical systems this multivalued perturbation comes from the Filippov regularization of a nonlinear discontinuous T-periodic term. Through the paper, assuming the existence of a T-periodic solution x~ε for ε > 0 small, under the condition that x0 is a nondegenerate cycle of the linearized unperturbed Hamiltonian system we provide a formula for the distance between any point x0(t) and the trajectories x~ε([0, T]) along a transversal direction to x0(t).