Relative topological entropy for actions of non-discrete groups on compact spaces in the context of cut and project schemes

In the study of aperiodic order via dynamical methods, topological entropy is an important concept. In this paper, parts of the theory, like Bowen’s formula for fibre wise entropy or the independence of the definition from the choice of a Van Hove sequence, are extended to actions of several non-discrete groups. To establish these results, we will show that the Ornstein-Weiss lemma is valid for all considered groups which appear in the study of cut and project schemes.