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

Bounemoura, Abed; Féjoz, Jacques (2017), KAM, α -Gevrey regularity and the α -Bruno-Rüssmann condition, Annali della Scuola Normale Superiore di Pisa. Classe di Scienze, p. 53. 10.2422/2036-2145.201707_009

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Type
Article accepté pour publication ou publié
Date
2017-06
Journal name
Annali della Scuola Normale Superiore di Pisa. Classe di Scienze
Publisher
Stampacchia Guido
Pages
53
Publication identifier
10.2422/2036-2145.201707_009
Metadata
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Author(s)
Bounemoura, Abed
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Institut de Mécanique Céleste et de Calcul des Ephémérides [IMCCE]
Féjoz, Jacques
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Institut de Mécanique Céleste et de Calcul des Ephémérides [IMCCE]
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.
Subjects / Keywords
Hamiltonian systems; Gevrey class; Bruno-R£ussmann vectors; stability; KAM theory

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