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

Pierre-Antoine Guihéneuf

• 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.