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

Xuanji  Hou; Lei  Jiao

doi:10.3934/dcds.2016.36.3125

Article Contents

2016, Volume 36, Issue 6: 3125-3152. Doi: 10.3934/dcds.2016.36.3125

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

Xuanji Hou^1, and
Lei Jiao^2,

1.
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079
2.
School of Science, Nanjing University of Science and Technology, Nanjing 210094

Received: June 2015

Revised: October 2015

Published: May 2017

Abstract / Introduction Related Papers Cited by

Abstract

We consider analytic cocycles on $\mathbb{T}^d\times U(n)$. We prove that, if a cocycle $(\alpha,A)$ with Diophantine $\alpha$ in an analytic class of radius $h$ can be conjugated to a constant cocycle $(\alpha,C)$ via some measurable conjugacy, then for almost all $C$, for any $h_*$ smaller than $h$, it can be conjugated to $(\alpha,C)$ in the analytic class of radius $h_*$, provided that $A$ is sufficiently close to some constant (the closeness depend only on $h-h_*$ and the Diophantine condition of $\alpha$).

Keywords:

Cocycles,
reducibility,
rigidity,
KAM.

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

Citation:

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References

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