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Reducibility of ultra-differentiable quasi-periodic cocycles under an adapted arithmetic condition

Bounemoura, Abed; Chavaudret, Claire; Liang, Shuqing (2019), Reducibility of ultra-differentiable quasi-periodic cocycles under an adapted arithmetic condition. https://basepub.dauphine.fr/handle/123456789/20691

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02408592
Date
2019
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
15
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Author(s)
Bounemoura, Abed
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Chavaudret, Claire
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
Laboratoire Jean Alexandre Dieudonné [JAD]
Liang, Shuqing
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We prove a reducibility result for sl(2,R) quasi-periodic cocycles close to a constant elliptic matrix in ultra-differentiable classes, under an adapted arithmetic condition which extends the Brjuno-Rüssmann condition in the analytic case. The proof is based on an elementary property of the fibered rotation number and deals with ultra- differentiable functions with a weighted Fourier norm. We also show that a weaker arithmetic condition is necessary for reducibility, and that it can be compared to a sufficient arithmetic condition.
Subjects / Keywords
quasi-periodic; cocycles; Lyapunov exponent; rotation number; reducibility