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Critical almost Mathieu operator: hidden singularity, gap continuity, and the Hausdorff dimension of the spectrum
We obtain a representation of the critical almost Mathieu family as a Jacobi matrix that has a singularity. This allows us to prove that the Hausdorff dimension of its spectrum is not larger than 1/2 for all irrational frequencies, solving a long-standing problem. Other corollaries include two very
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