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

2021/02/09 by Ge, Lingrui, Wang, Yiqian, You, Jiangong +1 · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2102.05175

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 \citeklein,cgyz. This shows that G² is the transition space for the continuity of the Lyapunov exponent.

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• Discontinuity of Lyapunov exponent in spaces of quasiperiodic cocycles: Smoothness vs Arithmetic

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