We prove the joint continuity of Lyapunov exponent in the energy and the Diophantine frequency for quasi-periodic Schrödinger cocycles with the C² cos-type potentials. In particular, the Lyapunov exponent is log-Hölder continuous at each Diophantine frequency.

中文翻译：

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有限光滑准周期薛定谔环的李雅普诺夫指数的联合连续性

我们证明了具有C ² cos 型势的准周期薛定谔共循环的能量和丢番图频率的 Lyapunov 指数的联合连续性。尤其是，李雅普诺夫指数在每个丢番图频率处都是对数保持连续的。