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

Veronica Baker[1]; Marcy Barge[1]; Jaroslaw Kwapisz[1]

  • [1] Montana State University Department of Mathematical Sciences Bozeman MT 59717-2400 (USA)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 7, page 2213-2248
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Baker, Veronica, Barge, Marcy, and Kwapisz, Jaroslaw. "Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to $\beta $-shifts." Annales de l’institut Fourier 56.7 (2006): 2213-2248. <http://eudml.org/doc/10202>.

@article{Baker2006,
abstract = {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.},
affiliation = {Montana State University Department of Mathematical Sciences Bozeman MT 59717-2400 (USA); Montana State University Department of Mathematical Sciences Bozeman MT 59717-2400 (USA); Montana State University Department of Mathematical Sciences Bozeman MT 59717-2400 (USA)},
author = {Baker, Veronica, Barge, Marcy, Kwapisz, Jaroslaw},
journal = {Annales de l’institut Fourier},
keywords = {Substitution; tilings; pure discrete spectrum spectrum; Pisot; substitution},
language = {eng},
number = {7},
pages = {2213-2248},
publisher = {Association des Annales de l’institut Fourier},
title = {Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to $\beta $-shifts},
url = {http://eudml.org/doc/10202},
volume = {56},
year = {2006},
}

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
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 7
SP - 2213
EP - 2248
AB - 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.
LA - eng
KW - Substitution; tilings; pure discrete spectrum spectrum; Pisot; substitution
UR - http://eudml.org/doc/10202
ER -

References

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