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2016 Some examples of repetitive, nonrectifiable Delone sets
María Cortez, Andrés Navas
Geom. Topol. 20(4): 1909-1939 (2016). DOI: 10.2140/gt.2016.20.1909


Burago and Kleiner and, independently, McMullen, gave examples of Delone sets (that is, subsets of Euclidean space that are discrete and separated in a uniform way) that are non-bi-Lipschitz equivalent to the standard lattice. We refine their methods of construction via a discretization technique, thus giving the first examples of Delone sets as above that are also repetitive, in the sense that a translated copy of each patch appears in every large enough ball.


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María Cortez. Andrés Navas. "Some examples of repetitive, nonrectifiable Delone sets." Geom. Topol. 20 (4) 1909 - 1939, 2016.


Received: 18 August 2014; Revised: 31 July 2015; Accepted: 26 August 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1378.37037
MathSciNet: MR3548461
Digital Object Identifier: 10.2140/gt.2016.20.1909

Primary: 37B50
Secondary: 52C22

Keywords: Invariant measures , nonrectifiable , repetitive Delone sets

Rights: Copyright © 2016 Mathematical Sciences Publishers

Vol.20 • No. 4 • 2016
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