Smooth quasiperiodic SL(2,\R)-cocycles (II)-Sharp transition space for the continuity of the Lyapunov exponent.

Abstract: We construct points of discontinuity of the Lyapunov exponent of quasiperiodic Shr\"odinger cocycles in Gevrey space $G^{s}$ with $s>2$. In contrast, the Lyapunov exponent has been proved to be continuous in $G^{s}$ with $s<2$ by Klein and Cheng-Ge-You-Zhou. This shows that $G^2$ is the transition space for the continuity of the Lyapunov exponent.

MathematicsPhysics

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UCI Mathematical Physics