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

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  • 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 $\alpha$).
    Mathematics Subject Classification: Primary: 37C15; Secondary: 37C05.


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