We show that the quasi-periodic Schrodinger cocycle with a continuous potential is of parabolic type, with a unique invariant section, at all gap edges where the Lyapunov exponent vanishes. This applies, in particular, to the almost Mathieu equation with critical coupling. It also provides examples of real-analytic cocycles having a unique invariant section which is not smooth.

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关于临界耦合处的几乎 Mathieu 方程的动力学的一些评论

我们表明，具有连续势的准周期薛定谔共循环是抛物线型的，在 Lyapunov 指数消失的所有间隙边缘处具有独特的不变截面。这尤其适用于具有临界耦合的几乎 Mathieu 方程。它还提供了具有不平滑的唯一不变截面的实解析共环的示例。