Non-degenerate Liouville tori are KAM stable
Bounemoura, Abed (2016), Non-degenerate Liouville tori are KAM stable, Advances in Mathematics, 292, p. 42-51. 10.1016/j.aim.2016.01.012
TypeArticle accepté pour publication ou publié
Journal nameAdvances in Mathematics
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CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)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 invariant tori are smooth (respectively Gevrey-smooth, respectively real-analytic). This answers a question raised in a recent work by Eliasson, Fayad and Krikorian . 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.
Subjects / KeywordsHamiltonian systems; KAM theory
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