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Characterization of model sets by dynamical systems

Published online by Cambridge University Press:  12 February 2007

MICHAEL BAAKE ,
DANIEL LENZ  and
ROBERT V. MOODY
MICHAEL BAAKE
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany (e-mail: [email protected])
DANIEL LENZ
Affiliation:
Fakultät für Mathematik, TU Chemnitz, 09107 Chemnitz, Germany (e-mail: [email protected])
ROBERT V. MOODY
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3P4, Canada (e-mail: [email protected])
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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 $\beta$ and then relate the properties of $\beta$ 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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 2 , April 2007 , pp. 341 - 382
Copyright
2007 Cambridge University Press

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