Almost reducibility for finitely differentiable SL(2,R)-valued quasi-periodic cocycles

Details Almost reducibility for finitely differentiable SL(2,R)-valued quasi-periodic cocycles Almost reducibility for finitely differentiable SL(2,R)-valued quasi-periodic cocycles

2010-11-08

arxiv.org/abs/1011.1765v3

Mathematics

Dynamical Systems

Scientific paper

Quasi-periodic cocycles with a diophantine frequency and with values in SL(2,R) are shown to be almost reducible as long as they are close enough to a constant, in the topology of k times differentiable functions, with k great enough. Almost reducibility is obtained by analytic approximation after a loss of differentiability which only depends on the frequency and on the constant part. As in the analytic case, if their fibered rotation number is diophantine or rational with respect to the frequency, such cocycles are in fact reducible. This extends Eliasson's theorem on Schr\"odinger cocycles to the differentiable case.

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