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arXiv · 2009.13607

Modulus of continuity for spectral measures of suspension flows over Salem type substitutions

Juan Marshall-Maldonado
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Abstract

We study the spectrum of the self-similar suspension flows of sub-shifts arising from primitive substitutions. We focus on the case where the substitution matrix has a Salem number {\alpha} as dominant eigenvalue. We obtain a H\"older exponent for the spectral measures for points away from zero and belonging to the field Q({\alpha}). This exponent depends only on three parameters of each of these points: its absolute value, the absolute value of its real conjugate and its denominator.

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Juan Marshall-Maldonado. 2020-09-28. Modulus of continuity for spectral measures of suspension flows over Salem type substitutions. https://arxiv.org/abs/2009.13607

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