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On embedding of repetitive Meyer multiple sets into model multiple sets

Published online by Cambridge University Press:  11 February 2015

JEAN-BAPTISTE AUJOGUE
JEAN-BAPTISTE AUJOGUE*
Affiliation:
Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France email [email protected]
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Abstract

Model sets are always Meyer sets but the converse is generally not true. In this work we show that for a repetitive Meyer multiple set of $\mathbb{R}^{d}$ with associated dynamical system $(\mathbb{X},\mathbb{R}^{d})$ , the property of being a model multiple set is equivalent to $(\mathbb{X},\mathbb{R}^{d})$ being almost automorphic. We deduce this by showing that a repetitive Meyer multiple set can always be embedded into a repetitive model multiple set having a smaller group of topological eigenvalues.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 6 , September 2016 , pp. 1679 - 1702
Copyright
© Cambridge University Press, 2015 

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