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

作者：Chavaudret Claire^*

来源：Nonlinearity, 2012, 25(2): 481-494.

DOI：10.1088/0951-7715/25/2/481

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 the fibred rotation number of these cocycles is diophantine or rational with respect to the frequency, they are in fact reducible. This extends Eliasson%26apos;s theorem on Schrodinger cocycles to the differentiable case.

• 出版日期2012-2