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arXiv · 1912.06411

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

Abed Bounemoura·Claire Chavaudret·Shuqing Liang
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Abstract

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-R{ü}ssmann 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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Abed Bounemoura, Claire Chavaudret, Shuqing Liang. 2019-12-13. Reducibility of ultra-differentiable quasi-periodic cocycles under an adapted arithmetic condition. https://arxiv.org/abs/1912.06411

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