Characterizations of model sets by dynamical systems
Dynamical Systems
2019-07-17 v2 Metric Geometry
Abstract
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 and then relate the properties of 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.
Cite
@article{arxiv.math/0511648,
title = {Characterizations of model sets by dynamical systems},
author = {Michael Baake and Daniel Lenz and Robert V. Moody},
journal= {arXiv preprint arXiv:math/0511648},
year = {2019}
}
Comments
41 pages, revised version