Linearly repetitive Delone sets are rectifiable

José Aliste-Prieto, Daniel Coronel, Jean Marc Gambaudo

Resultado de la investigación: Contribución a la publicaciónArticle

  • 8 Citas

Resumen

We show that every linearly repetitive Delone set in the Euclidean d-space Rd, with d≥2, is equivalent, up to a bi-Lipschitz homeomorphism, to the integer lattice Zd. In the particular case when the Delone set X in Rd comes from a primitive substitution tiling of Rd, we give a condition on the eigenvalues of the substitution matrix which ensures the existence of a homeomorphism with bounded displacement from X to the lattice βZd for some positive β. This condition includes primitive Pisot substitution tilings but also concerns a much broader set of substitution tilings.

Idioma originalEnglish
Páginas (desde - hasta)275-290
Número de páginas16
PublicaciónAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volumen30
Número de edición2
Identificadores de objetos digitales
EstadoPublished - 2013

Huella dactilar

Substitution
Tiling
Homeomorphism
Linearly
D-space
Lipschitz
Euclidean
Eigenvalue
Integer

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics

Citar esto

Aliste-Prieto, José; Coronel, Daniel; Gambaudo, Jean Marc / Linearly repetitive Delone sets are rectifiable.

En: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, Vol. 30, N.º 2, 2013, p. 275-290.

Resultado de la investigación: Contribución a la publicaciónArticle

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Linearly repetitive Delone sets are rectifiable. / Aliste-Prieto, José; Coronel, Daniel; Gambaudo, Jean Marc.

En: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, Vol. 30, N.º 2, 2013, p. 275-290.

Resultado de la investigación: Contribución a la publicaciónArticle

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