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Veronica Baker; Marcy Barge; Jaroslaw Kwapisz
Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to $\beta $-shifts
(Représentation géométrique et coïncidence pour pavages associés à une substitution de type Pisot non-unimodulaire réductible avec une application aux beta-shifts)
Annales de l'institut Fourier, 56 no. 7 (2006), p. 2213-2248, doi: 10.5802/aif.2238
Article PDF | Analyses MR 2290779 | Zbl 1138.37008 | 1 citation dans Cedram
Class. Math.: 37B50, 11R06, 28D05
Mots clés: substitution, pavages, spectre purement discret, Pisot

Résumé - Abstract

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.

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