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

Xuanji Hou, Georgi Popov

We consider the reducibility problem of cocycles $(\alpha ,A)$ on $\T^d\times U(n)$ in Gevrey classes, where $\alpha$ is a Diophantine vector. We prove that, if a Gevrey cocycle is conjugate…