A Characterization of Model Multi-colour Sets

Details A Characterization of Model Multi-colour Sets A Characterization of Model Multi-colour Sets

2005-10-20

arxiv.org/abs/math/0510426v1

Ann. Henri Poincare 7 (2006), no. 1, 125--143

Mathematics

Metric Geometry

23pages; to appear in Annales Henri Poincare

Scientific paper

10.1007/s00023-005-0244-6

Model sets are always Meyer sets, but not vice-versa. This article is about characterizing model sets (general and regular) amongst the Meyer sets in terms of two associated dynamical systems. These two dynamical systems describe two very different topologies on point sets, one local and one global. In model sets these two are strongly interconnected and this connection is essentially definitive. The paper is set in the context of multi-colour sets, that is to say, point sets in which points come in a finite number of colours, that are loosely coupled together by finite local complexity.

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