English

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 β\beta and then relate the properties of β\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.

Keywords

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