Transition space for the continuity of the Lyapunov exponent of quasiperiodic Schrödinger cocycles

Lingrui Ge, Yiqian Wang, Jiangong You, Xin Zhao

Published 2021-02-09Version 1

We construct discontinuous point of the Lyapunov exponent of quasiperiodic Schr\"odinger cocycles in the Gevrey space $G^{s}$ with $s>2$. In contrast, the Lyapunov exponent has been proved to be continuous in the Gevrey space $G^{s}$ with $s<2$ \cite{klein,cgyz}. This shows that $G^2$ is the transition space for the continuity of the Lyapunov exponent.