- 12-100 Livia Corsi, Roberto Feola, Guido Gentile
- Lower-dimensional invariant tori for perturbations of a class of non-convex Hamiltonian functions
Sep 13, 12
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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.