%0 Journal Article
%T Tower systems for Linearly repetitive Delone sets
%A Jos¨¦ Aliste-Prieto
%A Daniel Coronel
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1003.4309v1