Non-degenerate Liouville tori are KAM stable
Résumé
In this short note, we prove that a quasi-periodic torus, with a non-resonant frequency (that can be Diophantine or Liouville) and which is invariant by a sufficiently regular Hamiltonian flow, is KAM stable provided it is Kolmogorov non-degenerate. When the Hamiltonian is smooth (respectively Gevrey-smooth, respectively real-analytic), the in-variant tori are smooth (respectively Gevrey-smooth, respectively real-analytic). This answers a question raised in a recent work by Eliasson, Fayad and Krikorian ([EFK]). We also take the opportunity to ask other questions concerning the stability of non-resonant invariant quasi-periodic tori in (analytic or smooth) Hamiltonian systems.
Domaines
Systèmes dynamiques [math.DS]Origine | Fichiers produits par l'(les) auteur(s) |
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