Model sets are always Meyer sets but the converse is generally not true. In this work we show that for a repetitive Meyer multiple sets of $\mathbb{ R}^d$ with associated dynamical system $(\mathbb{ X}, \mathbb{ R}^d)$, the property of being a model multiple set is equivalent for $(\mathbb{ X}, \mathbb{ R}^d)$ to be 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.
Categories: math.DS