H\"older continuity of the Lyapunov exponent for Schr\"odinger cocycle with quasi-periodic Gevrey potential and weak Liouville frequency

TL;DR

This paper extends the known H"older continuity of the Lyapunov exponent from analytic to Gevrey potentials in quasi-periodic Schr"odinger cocycles with weak Liouville frequency, broadening the class of potentials for which regularity is established.

Contribution

It proves H"older continuity of the Lyapunov exponent for Gevrey potentials, generalizing previous results from analytic potentials in the context of weak Liouville frequency.

Findings

H"older continuity holds for Gevrey potentials

Extension of regularity results from analytic to Gevrey class

Applicable to Schr"odinger cocycles with weak Liouville frequency

Abstract

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