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Some remarks on the optimality of the Bruno-Rüssmann condition

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Date
2018
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-01679497
Dewey
Analyse
Sujet
Bruno-Rüssmann condition; Systèmes dynamiques
URI
https://basepub.dauphine.fr/handle/123456789/17521
Collections
  • CEREMADE : Publications
Metadata
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Author
Bounemoura, Abed
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Bounemoura, Abed
Type
Document de travail / Working paper
Item number of pages
12
Abstract (EN)
We prove that the Bruno-Rüssmann condition is optimal for the analytic preservation of a quasi-periodic invariant curve for an analytic twist map. The proof is based on Yoccoz's corresponding result for analytic circle diffeomorphisms and the uniqueness of invariant curves with a given irrational rotation number. We also prove a similar result for analytic Tonelli Hamiltonian flow with n = 2 degrees of freedom; for n ≥ 3 we only obtain a weaker result which recovers and slightly improves a theorem of Bessi.

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