TY - JOUR
T1 - Tower systems for linearly repetitive Delone sets
AU - Aliste-Prieto, José
AU - Coronel, Daniel
N1 - Publisher Copyright:
Copyright © Cambridge University Press 2010.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2011/12/1
Y1 - 2011/12/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=78449232340&partnerID=8YFLogxK
U2 - 10.1017/S0143385710000507
DO - 10.1017/S0143385710000507
M3 - Article
AN - SCOPUS:78449232340
SN - 0143-3857
VL - 31
SP - 1595
EP - 1618
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 6
ER -