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Non-degenerate Liouville tori are KAM stable

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LiouvilleTori.pdf (223.0Kb)
Date
2016
Dewey
Analyse
Sujet
Hamiltonian systems; KAM theory
Journal issue
Advances in Mathematics
Volume
292
Publication date
04-2016
Article pages
42-51
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.aim.2016.01.012
URI
https://basepub.dauphine.fr/handle/123456789/20229
Collections
  • CEREMADE : Publications
Metadata
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Author
Bounemoura, Abed
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
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 [6]. 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.

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