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. © 2013 Springer Science+Business Media New York.
|Titolo:||Lower-Dimensional Invariant Tori for Perturbations of a Class of Non-convex Hamiltonian Functions|
|Autori:||Livia Corsi; Roberto Feola; Guido Gentile|
|Data di pubblicazione:||2013|
|Digital Object Identifier (DOI):||10.1007/s10955-012-0682-8|
|Appare nelle tipologie:||1.1 Journal article|