Characterization of model sets by dynamical systems | Ergodic Theory and Dynamical Systems | Cambridge Core (original) (raw)
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Published online by Cambridge University Press: 12 February 2007
MICHAEL BAAKE
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany (e-mail: mbaake@math.uni-bielefeld.de)
DANIEL LENZ
Affiliation:
Fakultät für Mathematik, TU Chemnitz, 09107 Chemnitz, Germany (e-mail: dlenz@mathematik.tu-chemnitz.de)
ROBERT V. MOODY
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3P4, Canada (e-mail: rmoody@uvic.ca)
Abstract
It is shown how regular model sets can be characterized in terms of the 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\betabeta and then relate the properties of beta\betabeta to those 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.
Information
Type
Research Article
Copyright
2007 Cambridge University Press
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