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Pré-Publication, Document De Travail Année : 2013

On the modulus of continuity for spectral measures in substitution dynamics

Résumé

The paper gives first quantitative estimates on the modulus of continuity of the spectral measure for weakly mixing suspension flows over substitution automorphisms. The main results are, first, a Hoelder estimate for the spectral measure of almost all suspension flows with a piecewise constant roof function; second, a log-Hoelder estimate for self-similar suspension flows; and, third, a Hoelder asymptotic expansion of the spectral measure at zero for such flows. The second result implies log-Hoelder estimates for the spectral measures of translation flows along stable foliations of pseudo-Anosov automorphisms. The Appendix explains the connection of these results with the theory of Bernoulli convolutions.

Dates et versions

hal-00957665 , version 1 (10-03-2014)

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Alexander I. Bufetov, Boris Solomyak. On the modulus of continuity for spectral measures in substitution dynamics. 2013. ⟨hal-00957665⟩
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