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Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to $β$ -shifts

Veronica Baker; Marcy Barge; Jaroslaw Kwapisz — 2006

Annales de l’institut Fourier

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.

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Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to β -shifts

Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to $β$ -shifts