Non-degenerate Liouville tori are KAM stableReport as inadecuate

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1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Abstract : 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.

Author: Abed Bounemoura -



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