We consider a class of quasi-integrable Hamiltonian systems obtained by adding to a non-convex Hamiltonian function of an integrable system a perturbation depending only on the angle variables. We focus on a resonant maximal torus of the unperturbed system, foliated into a family of lower-dimensional tori of codimension 1, invariant under a quasi-periodic flow with rotation vector satisfying some mild Diophantine condition. We show that at least one lower-dimensional torus with that rotation vector always exists also for the perturbed system. The proof is based on multiscale analysis and resummation procedures of divergent series. A crucial role is played by suitable symmetries and cancellations, ultimately due to the Hamiltonian structure of the system.

Corsi, L., Feola, R., Gentile, G. (2013). Lower-dimensional invariant tori for perturbations of a class of non-convex Hamiltonian functions. JOURNAL OF STATISTICAL PHYSICS, 150(1), 156-180 [10.1007/s10955-012-0682-8].

Lower-dimensional invariant tori for perturbations of a class of non-convex Hamiltonian functions

CORSI L;FEOLA R;GENTILE, Guido
2013-01-01

Abstract

We consider a class of quasi-integrable Hamiltonian systems obtained by adding to a non-convex Hamiltonian function of an integrable system a perturbation depending only on the angle variables. We focus on a resonant maximal torus of the unperturbed system, foliated into a family of lower-dimensional tori of codimension 1, invariant under a quasi-periodic flow with rotation vector satisfying some mild Diophantine condition. We show that at least one lower-dimensional torus with that rotation vector always exists also for the perturbed system. The proof is based on multiscale analysis and resummation procedures of divergent series. A crucial role is played by suitable symmetries and cancellations, ultimately due to the Hamiltonian structure of the system.
Corsi, L., Feola, R., Gentile, G. (2013). Lower-dimensional invariant tori for perturbations of a class of non-convex Hamiltonian functions. JOURNAL OF STATISTICAL PHYSICS, 150(1), 156-180 [10.1007/s10955-012-0682-8].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/134661
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