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Published on 21 Oct 2025

Multifractal Analysis of Spectral Measures for Sturmian Hamiltonians and the Almost Mathieu Operator

We investigate the multifractal structure of the density of states measure for Sturmian Hamiltonians, as well as the absolutely continuous spectral measures of almost Mathieu operators (AMO). For the density of states measure, by establishing the $C^1$ smoothness and strict convexity of the relative topological pressure on $(0,\infty)$, we prove that the multifractal formalism holds for Lebesgue almost every $\alpha$. For the absolutely continuous spectral measure of the subcritical AMO, by integrating continued–fraction/metric Diophantine techniques with refined covering arguments, we provide a full description of the multifractal spectrum and a more refined analysis in the logarithmic gauge.