RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mosc. Math. J.: Year: Volume: Issue: Page: Find

 Mosc. Math. J., 2017, Volume 17, Number 1, Pages 35–49 (Mi mmj624)

Spectral measure at zero for self-similar tilings

Jordan Emme

Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France

Abstract: 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.

DOI: https://doi.org/10.17323/1609-4514-2017-17-1-35-49

Full text: http://www.mathjournals.org/.../2017-017-001-003.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 37B50, 37A30
Received: June 10, 2016; in revised form January 24, 2017
Language:

Citation: Jordan Emme, “Spectral measure at zero for self-similar tilings”, Mosc. Math. J., 17:1 (2017), 35–49

Citation in format AMSBIB
\Bibitem{Emm17} \by Jordan~Emme \paper Spectral measure at zero for self-similar tilings \jour Mosc. Math.~J. \yr 2017 \vol 17 \issue 1 \pages 35--49 \mathnet{http://mi.mathnet.ru/mmj624} \crossref{https://doi.org/10.17323/1609-4514-2017-17-1-35-49} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3634519} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000402641900003}