Spectral measure at zero for self-similar tilings
Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France
The goal of this paper is to study the action of the group of translations over self-similar tilings in the Euclidean space $\mathbb R^d$. It investigates the behaviour near zero of spectral measures for such dynamical systems. Namely, the paper gives a Hölder asymptotic expansion near zero for these spectral measures. It is a generalization to higher dimension of a result by Bufetov and Solomyak who studied self similar-suspension flows for substitutions. The study of such asymptotics mostly involves the understanding of the deviations of some ergodic averages.
Key words and phrases:
self-similar tilings, ergodic theory, spectral measures.
MSC: 37B50, 37A30
Received: June 10, 2016; in revised form January 24, 2017
Jordan Emme, “Spectral measure at zero for self-similar tilings”, Mosc. Math. J., 17:1 (2017), 35–49
Citation in format AMSBIB
\paper Spectral measure at zero for self-similar tilings
\jour Mosc. Math.~J.
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