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KAM, α -Gevrey regularity and the α -Bruno-Rüssmann condition

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Date
2017-06
Dewey
Analyse
Sujet
Hamiltonian systems; Gevrey class; Bruno-R£ussmann vectors; stability; KAM theory
Journal issue
Annali della Scuola Normale Superiore di Pisa. Classe di Scienze
Publication date
2018
Article pages
53
Publisher
Stampacchia Guido
DOI
http://dx.doi.org/10.2422/2036-2145.201707_009
Forthcoming
oui
URI
https://basepub.dauphine.fr/handle/123456789/18366
Collections
  • CEREMADE : Publications
Metadata
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Author
Bounemoura, Abed
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
153 Institut de Mécanique Céleste et de Calcul des Ephémérides [IMCCE]
Féjoz, Jacques
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
153 Institut de Mécanique Céleste et de Calcul des Ephémérides [IMCCE]
Type
Article accepté pour publication ou publié
Abstract (EN)
We prove a new invariant torus theorem, for α-Gevrey smooth Hamiltonian systems , under an arithmetic assumption which we call the α-Bruno-Rüssmann condition , and which reduces to the classical Bruno-Rüssmann condition in the analytic category. Our proof is direct in the sense that, for analytic Hamiltonians, we avoid the use of complex extensions and, for non-analytic Hamiltonians, we do not use analytic approximation nor smoothing operators. Following Bessi, we also show that if a slightly weaker arithmetic condition is not satisfied, the invariant torus may be destroyed. Crucial to this work are new functional estimates in the Gevrey class.

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