For subcritical almost Mathieu operators with Diophantine frequency, each exceptional lower-scaling-index level set has Hausdorff dimension 0 but log-Hausdorff dimension 1.
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Log-Hausdorff multifractality of the absolutely continuous spectral measure of the almost Mathieu operator
For subcritical almost Mathieu operators with Diophantine frequency, each exceptional lower-scaling-index level set has Hausdorff dimension 0 but log-Hausdorff dimension 1.