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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Linearly repetitive Delone systems have a finite number of nonperiodic Delone system factors


Authors: María Isabel Cortez, Fabien Durand and Samuel Petite
Journal: Proc. Amer. Math. Soc. 138 (2010), 1033-1046
MSC (2010): Primary 37B50
Published electronically: November 2, 2009
MathSciNet review: 2566569
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Abstract: In this paper we prove linearly repetitive Delone systems have finitely many Delone system factors up to conjugacy. This result is also applicable to linearly repetitive tiling systems.


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María Isabel Cortez
Affiliation: Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Avenida Libertador Bernardo O’Higgins 3363, Santiago, Chile
Email: maria.cortez@usach.cl

Fabien Durand
Affiliation: Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, CNRS-UMR 6140, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens Cedex, France
Email: fabien.durand@u-picardie.fr

Samuel Petite
Affiliation: Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, CNRS-UMR 6140, Université de Picardie Jules Verne, 33 rue Saint Leu, 80039 Amiens Cedex, France
Email: samuel.petite@u-picardie.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10139-9
PII: S 0002-9939(09)10139-9
Keywords: Delone sets, tiling systems, factor maps, linearly repetitive, Vorono\"{\i } cell.
Received by editor(s): December 8, 2008
Received by editor(s) in revised form: July 29, 2009
Published electronically: November 2, 2009
Communicated by: Bryna Kra
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.