Moscow Mathematical Journal

Volume 17, Issue 1, January–March 2017 pp. 35–49.

Spectral Measure at Zero for Self-Similar Tilings

Authors: Jordan Emme (1)
Author institution:(1) Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France

Summary:

The goal of this paper is to study the action of the group of translations over self-similar tilings in the Euclidean space 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.

2010 Math. Subj. Class. 37B50, 37A30.

Keywords: Self-similar tilings, ergodic theory, spectral measures.

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