Spectral measure at zero for self-similar tilings
Dynamical Systems
2017-10-24 v2 Spectral Theory
Abstract
The goal of this paper is to study the action of the group of translations over self-similar tilings in the euclidian space . It investigates the behaviour near zero for spectral measures for such dynamical systems. Namely the paper gives a H\"older 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.
Cite
@article{arxiv.1606.02470,
title = {Spectral measure at zero for self-similar tilings},
author = {Jordan Emme},
journal= {arXiv preprint arXiv:1606.02470},
year = {2017}
}