Tower systems for Linearly repetitive Delone sets

Details Tower systems for Linearly repetitive Delone sets Tower systems for Linearly repetitive Delone sets

2010-03-22

arxiv.org/abs/1003.4309v1

Mathematics

Dynamical Systems

27 pages, 2 figures.

Scientific paper

In this paper we study linearly repetitive Delone sets and prove, following the work of Bellissard, Benedetti and Gambaudo, that the hull of a linearly repetitive Delone set admits a properly nested sequence of box decompositions (tower system) with strictly positive and uniformly bounded (in size and norm) transition matrices. This generalizes a result of Durand for linearly recurrent symbolic systems. Furthermore, we apply this result to give a new proof of a classic estimation of Lagarias and Pleasants on the rate of convergence of patch-frequencies.

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