Presque r\'eductibilit\'e des cocycles quasi-p\'eriodiques de classe Gevrey 2

TL;DR

This paper proves that Gevrey 2 quasi-periodic cocycles with Diophantine frequency, near constant, are almost reducible, extending Eliasson's theorem from analytic to Gevrey class cocycles.

Contribution

It extends the almost reducibility result from analytic to Gevrey 2 class cocycles for classical Lie groups.

Findings

Gevrey 2 cocycles are almost reducible near constant.

Extension of Eliasson's theorem to Gevrey class.

Applicable to classical Lie groups.

Abstract

Gevrey 2 quasi-periodic cocycles with diophantine frequency, close to a constant, with values in classical Lie groups, are almost reducible in a weak sense. This is the analogue of Eliasson's almost reducibility theorem for analytic cocycles.