Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to β-shifts
Annales de l'Institut Fourier, Volume 56 (2006) no. 7, pp. 2213-2248.

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.

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.

DOI: 10.5802/aif.2238
Classification: 37B50,  11R06,  28D05
Keywords: Substitution, tilings, pure discrete spectrum spectrum, Pisot
Baker, Veronica 1; Barge, Marcy 1; Kwapisz, Jaroslaw 1

1 Montana State University Department of Mathematical Sciences Bozeman MT 59717-2400 (USA)
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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, Volume 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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