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We construct discontinuous point of the Lyapunov exponent of quasiperiodicSchr\"odinger cocycles in the Gevrey space $G^{s}$ with $s>2$. In contrast, theLyapunov 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 forthe continuity of the Lyapunov exponent.

Transition space for the continuity of the Lyapunov exponent of quasiperiodic Schr\"odinger cocycles