Zero Hausdorff dimension spectrum for the almost Mathieu operator

Abstract

We study the almost Mathieu operator at critical coupling. We prove that there exists a dense $G_{\delta }$ set of frequencies for which the spectrum is of zero Hausdorff dimension.

v1: 24 pp. v2: 25 pp, corrected the statement of Theorem 3 and added explanations in the proof of Theorem 2

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