Aim of the paper is to provide a method to analyze the behavior of -periodic solutions , of a perturbed planar Hamiltonian system near a cycle~, of smallest period , of the unperturbed system. The perturbation is represented by a -periodic multivalued map which vanishes as . In several problems from nonsmooth mechanical systems this multivalued perturbation comes from the Filippov regularization of a nonlinear discontinuous -periodic term. \noindent Through the paper, assuming the existence of a -periodic solution for small, under the condition that is a nondegenerate cycle of the linearized unperturbed Hamiltonian system we provide a formula for the distance between any point and the trajectories along a transversal direction to $x_0(t).
Cite this article
Oleg Makarenkov, Luisa Malaguti, Paolo Nistri, On the Behavior of Periodic Solutions of Planar Autonomous Hamiltonian Systems with Multivalued Periodic Perturbations. Z. Anal. Anwend. 30 (2011), no. 2, pp. 129–144DOI 10.4171/ZAA/1428