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Abstract: In this paper we study linearly repetitive Delone sets and prove, followingthe work of Bellissard, Benedetti and Gambaudo, that the hull of a linearlyrepetitive Delone set admits a properly nested sequence of box decompositionstower system with strictly positive and uniformly bounded in size and normtransition matrices. This generalizes a result of Durand for linearly recurrentsymbolic systems. Furthermore, we apply this result to give a new proof of aclassic estimation of Lagarias and Pleasants on the rate of convergence ofpatch-frequencies.



Author: José Aliste-Prieto, Daniel Coronel

Source: https://arxiv.org/







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