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June  2009, 24(2): 441-454. doi: 10.3934/dcds.2009.24.441

Local rigidity of reducibility of analytic quasi-periodic cocycles on $U(n)$

Xuanji Hou 1, and  Jiangong You 1,

1. 

Department of Mathematics, Nanjing University, Nanjing 210093, China

Received  March 2008 Revised  October 2008 Published  March 2009

In this paper, we consider the analytic reducibility problem of an analytic $d-$dimensional quasi-periodic cocycle $(\alpha,\ A)$ on $U(n)$ where $ \alpha$ is a Diophantine vector. We prove that, if the cocycle is conjugated to a constant cocycle $(\alpha,\ C)$ by a measurable conjugacy $(0,\ B)$, then for almost all $C$ it is analytically conjugated to $(\alpha,\ C)$ provided that $A$ is sufficiently close to some constant. Moreover $B$ is actually analytic if it is continuous.
Keywords: Reducibility, Rigidity, KAM., Almost reducibility.
Mathematics Subject Classification: Primary: 37C15; Secondary: 37C0.
Citation: Xuanji Hou, Jiangong You. Local rigidity of reducibility of analytic quasi-periodic cocycles on $U(n)$. Discrete & Continuous Dynamical Systems - A, 2009, 24 (2) : 441-454. doi: 10.3934/dcds.2009.24.441
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