Aim of the paper is to provide a method to analyze the behavior of T-periodic solutions x(epsilon), epsilon > 0, of a perturbed planar Hamiltonian system near a cycle x(0), of smallest period T, of the unperturbed system. The perturbation is represented by a T-periodic multivalued map which vanishes as epsilon -> 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(epsilon) for epsilon > 0 small, under the condition that x(0) is a nondegenerate cycle of the linearized unperturbed Hamiltonian system we provide a formula for the distance between any point x(0)(t) and the trajectories x(epsilon)([0, T)) along a transversal direction to x(0)(t).

O., M., L., M., Nistri, P. (2011). On the behavior of periodic solutions of planar autonomous Hamiltonian systems with multivalued periodic perturbations. JOURNAL OF ANALYSIS AND APPLICATIONS, 30(2), 129-144 [10.4171/ZAA/1428].

On the behavior of periodic solutions of planar autonomous Hamiltonian systems with multivalued periodic perturbations

NISTRI, PAOLO
2011-01-01

Abstract

Aim of the paper is to provide a method to analyze the behavior of T-periodic solutions x(epsilon), epsilon > 0, of a perturbed planar Hamiltonian system near a cycle x(0), of smallest period T, of the unperturbed system. The perturbation is represented by a T-periodic multivalued map which vanishes as epsilon -> 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(epsilon) for epsilon > 0 small, under the condition that x(0) is a nondegenerate cycle of the linearized unperturbed Hamiltonian system we provide a formula for the distance between any point x(0)(t) and the trajectories x(epsilon)([0, T)) along a transversal direction to x(0)(t).
2011
O., M., L., M., Nistri, P. (2011). On the behavior of periodic solutions of planar autonomous Hamiltonian systems with multivalued periodic perturbations. JOURNAL OF ANALYSIS AND APPLICATIONS, 30(2), 129-144 [10.4171/ZAA/1428].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/7031
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