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2008 International Workshop on Dynamical System and Realted Topics
(2008 / vol.10 / no.2)
Model sets in terms of two associated dynamical systems
Jeong-Yup Lee
Pages. 101-103   



Model sets, or cut and project sets, are an essential ingredient in the study of long-range aperiodic order and in both theoretical and experimental sides of quasicrystal theory. We introduce two very different topologies on point sets, one local and one global, and consider two associated dynamical systems. There is no reason to expect there to be any relationship between these two. However, in model sets these two dynamical systems are strongly interconnected and this connection is essentially definitive. We characterize the model set in terms of the two associated dynamical systems.