# American Institute of Mathematical Sciences

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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 $U(n)$

 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.
Citation: Xuanji Hou, Jiangong You. Local rigidity of reducibility of analytic quasi-periodic cocycles on $U(n)$. Discrete & Continuous Dynamical Systems, 2009, 24 (2) : 441-454. doi: 10.3934/dcds.2009.24.441
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