Model sets, almost periodic patterns, uniform density and linear maps

  • Pierre-Antoine Guihéneuf

    Universidade Federal Fluminense, Niteroi, Brasil, and Université Pierre et Marie Curie, Paris, France
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Abstract

This article consists in two relatively independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they are almost periodic patterns and thus possess a uniform density. In the second part, we prove that the class of model sets and almost periodic patterns are stable under discretizations of linear maps.

Cite this article

Pierre-Antoine Guihéneuf, Model sets, almost periodic patterns, uniform density and linear maps. Rev. Mat. Iberoam. 34 (2018), no. 1, pp. 455–474

DOI 10.4171/RMI/992