2010/01/10 by Makarenkov, Oleg, Malaguti, Luisa, Nistri, Paolo
#34A60 #34C25 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.1001.1568
Aim of the paper is to provide a method to analyze the behavior of T-periodic solutions x_\eps, \eps>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 \eps→0. In several problems from nonsmooth mechanical systems this multivalued perturbation comes from the Filippov regularization of a nonlinear discontinuous T-periodic term. \noindent Through the paper, assuming the existence of a T-periodic solution x_\eps for \eps>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_\eps([0,T]) along a transversal direction to x0(t).