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

Xuanji Hou; Jiangong You

doi:10.3934/dcds.2009.24.441

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2009, Volume 24, Issue 2: 441-454. Doi: 10.3934/dcds.2009.24.441

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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

Received: February 29, 2008

Revised: September 30, 2008

Published: May 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 37C15; Secondary: 37C05.

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