[Représentation géométrique et coïncidence pour pavages associés à une substitution de type Pisot non-unimodulaire réductible avec une application aux beta-shifts]
Cet article est consacré à l’étude du flot de translation sur pavages auto-similaires associés à une substitution de type Pisot. Nous construisons une représentation géométrique et nous donnons les conditions nécessaires et suffisantes pour que le flot ait un spectre purement discret. Dans l’application, nous montrons que pour certains beta-shifts, l’extension naturelle est naturellement isomorphique à un automorphisme du tore.
This article is devoted to the study of the translation flow on self-similar tilings associated with a substitution of Pisot type. We construct a geometric representation and give necessary and sufficient conditions for the flow to have pure discrete spectrum. As an application we demonstrate that, for certain beta-shifts, the natural extension is naturally isomorphic to a toral automorphism.
Keywords: Substitution, tilings, pure discrete spectrum spectrum, Pisot
Mot clés : substitution, pavages, spectre purement discret, Pisot
@article{AIF_2006__56_7_2213_0,
author = {Baker, Veronica and Barge, Marcy and Kwapisz, Jaroslaw},
title = {Geometric realization and coincidence for reducible non-unimodular {Pisot} tiling spaces with an application to $\beta $-shifts},
journal = {Annales de l'Institut Fourier},
pages = {2213--2248},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {56},
number = {7},
year = {2006},
doi = {10.5802/aif.2238},
zbl = {1138.37008},
mrnumber = {2290779},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/aif.2238/}
}
TY - JOUR AU - Baker, Veronica AU - Barge, Marcy AU - Kwapisz, Jaroslaw TI - Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to $\beta $-shifts JO - Annales de l'Institut Fourier PY - 2006 SP - 2213 EP - 2248 VL - 56 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2238/ DO - 10.5802/aif.2238 LA - en ID - AIF_2006__56_7_2213_0 ER -
%0 Journal Article %A Baker, Veronica %A Barge, Marcy %A Kwapisz, Jaroslaw %T Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to $\beta $-shifts %J Annales de l'Institut Fourier %D 2006 %P 2213-2248 %V 56 %N 7 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2238/ %R 10.5802/aif.2238 %G en %F AIF_2006__56_7_2213_0
Baker, Veronica; Barge, Marcy; Kwapisz, Jaroslaw. Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to $\beta $-shifts. Annales de l'Institut Fourier, Tome 56 (2006) no. 7, pp. 2213-2248. doi : 10.5802/aif.2238. http://archive.numdam.org/articles/10.5802/aif.2238/
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