Hölder continuity of the Lyapunov exponent for Schrödinger cocycle with quasi-periodic Gevrey potential and weak Liouville frequency

Abstract

For analytic quasi-periodic Schrödinger cocycles, You and Zhang [9] proved that the Lyapunov exponent is Hölder continuous for weak Liouville frequency. In this paper, we prove that the Hölder continuity also holds if the analytic potential is weakened to Gevrey potential.