On embedding of repetitive Meyer multiple sets into model multiple sets

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.