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arXiv · 1307.2954

Rigidity of the Reducibility of Gevrey Quasi-periodic Cocycles on U(n)

Xuanji Hou·Georgi Popov
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Abstract

We consider the reducibility problem of cocycles $(α,A)$ on $\T^d\times U(n)$ in Gevrey classes, where $ α$ is a Diophantine vector. We prove that, if a Gevrey cocycle is conjugated to a constant cocycle $(α,C)$ by a suitable measurable conjugacy $(0,B)$, then for almost all $C$ it can be conjugated to $(α,C)$ in the same Gevrey class, provided that $A$ is sufficiently close to a constant. If $B$ is continuous we obtain it is Gevrey smooth. We consider as well the global problem of reducibility in Gevrey classes when $d=1$.

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Xuanji Hou, Georgi Popov. 2013-07-11. Rigidity of the Reducibility of Gevrey Quasi-periodic Cocycles on U(n). https://arxiv.org/abs/1307.2954

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