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Model sets, almost periodic patterns, uniform density and linear maps (1512.00650v1)
Published 2 Dec 2015 in math.DS, cs.DM, and math.MG
Abstract: This article consists in two 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.