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
External document linkhttps://arxiv.org/abs/1412.0509v1
Journal nameAdvances in Mathematics
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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 regularHamiltonian flow, is KAM stable provided it is Kolmogorov non-degenerate. When theHamiltonian is smooth (respectively Gevrey-smooth, respectively real-analytic), the in-variant tori are smooth (respectively Gevrey-smooth, respectively real-analytic). Thisanswers a question raised in a recent work by Eliasson, Fayad and Krikorian ([EFK]). Wealso take the opportunity to ask other questions concerning the stability of non-resonantinvariant quasi-periodic tori in (analytic or smooth) Hamiltonian systems.
Subjects / KeywordsKAM theorem; Hamiltonian systems
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