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

Abstract

We construct discontinuous point of the Lyapunov exponent of quasiperiodic Schrödinger 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.

27 pages

References in corpus (3)

• The absolutely continuous spectrum of the almost Mathieu operator
• Hölder regularity of the integrated density of states for quasi-periodic long-range operators on ${\ell }^2({\mathbb{Z}}^d)$
• Global rigidity for ultra-differentiable quasiperiodic cocycles and its spectral applications

Cited by in corpus (1)

• Global rigidity for ultra-differentiable quasiperiodic cocycles and its spectral applications