Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems |
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Authors: | Xuanji Hou Jiangong You |
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Institution: | 1.Department of Mathematics,Nanjing University,Nanjing,P.R. China;2.School of Mathematics and Statistics,Huazhong Normal University,Wuhan,P.R. China |
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Abstract: | In this paper, we prove that a quasi-periodic linear differential equation in sl(2,?) with two frequencies (α,1) is almost reducible provided that the coefficients are analytic and close to a constant. In the case that α is Diophantine we get the non-perturbative reducibility. We also obtain the reducibility and the rotations reducibility for an arbitrary irrational α under some assumption on the rotation number and give some applications for Schrödinger operators. Our proof is a generalized KAM type iteration adapted to all irrational α. |
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