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Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2021

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

Résumé

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.
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Dates et versions

hal-02408592 , version 1 (13-12-2019)

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Citer

Abed Bounemoura, Claire Chavaudret, Shuqing Liang. Reducibility of ultra-differentiable quasi-periodic cocycles under an adapted arithmetic condition. Proceedings of the American Mathematical Society, 2021, 149 (7), pp.2999-3012. ⟨10.1090/PROC/15433⟩. ⟨hal-02408592⟩
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