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

Bounemoura, Abed; Chavaudret, Claire; Liang, Shuqing (2021), Reducibility of ultra-differentiable quasi-periodic cocycles under an adapted arithmetic condition, Proceedings of the American Mathematical Society, 151, 4, p. 2999-3012

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Type
Article accepté pour publication ou publié
Date
2021
Journal name
Proceedings of the American Mathematical Society
Volume
151
Number
4
Publisher
American Mathematical Society
Published in
Paris
Pages
2999-3012
Metadata
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Author(s)
Bounemoura, Abed
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Chavaudret, Claire
Laboratoire Jean Alexandre Dieudonné [LJAD]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
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