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

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.