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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Some examples of repetitive, nonrectifiable Delone sets

María Isabel Cortez and Andrés Navas

Geometry & Topology 20 (2016) 1909–1939
Abstract

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.

Keywords
repetitive Delone sets, nonrectifiable, invariant measures
Mathematical Subject Classification 2010
Primary: 37B50
Secondary: 52C22
References
Publication
Received: 18 August 2014
Revised: 31 July 2015
Accepted: 26 August 2015
Published: 15 September 2016
Proposed: Steve Ferry
Seconded: Bruce Kleiner, John Lott
Authors
María Isabel Cortez
Departamento de Matemáticas, Facultad de Ciencias
Universidad de Santiago de Chile
Alameda 3363
Estación Central
9170022 Santiago
Chile
Andrés Navas
Departamento de Matemáticas, Facultad de Ciencias
Universidad de Santiago de Chile
Alameda 3363, Estación Central
9170022 Santiago
Chile