Mathematics – Dynamical Systems
Scientific paper
2005-11-27
Mathematics
Dynamical Systems
41 pages, revised version
Scientific paper
It is shown how regular model sets can be characterized in terms of regularity properties of their associated dynamical systems. The proof proceeds in two steps. First, we characterize regular model sets in terms of a certain map $\beta$ and then relate the properties of $\beta$ to ones of the underlying dynamical system. As a by-product, we can show that regular model sets are, in a suitable sense, as close to periodic sets as possible among repetitive aperiodic sets.
Baake Michael
Lenz Daniel
Moody Robert V.
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