Almost reducibility of quasiperiodic sl(2, R)-cocycles in ultradifferentiable classes

Abstract

Given a quasiperiodic cocycle in sl(2, R) sufficiently close to a constant, we prove that it is almost-reducible in ultradifferentiable class under an adapted arithmetic condition on the frequency vector. We also give a corollary on the Hölder regularity of the Lyapunov exponent.