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.

arXiv comment27 pages

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Cited by in corpus (1)

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