Linearly repetitive delone sets

José Aliste Prieto, Daniel Coronel, María Isabel Cortez, Fabien Durand, Samuel Petite

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

7 Citations (Scopus)

Abstract

Linearly repetitive Delone sets are the simplest aperiodic repetitive Delone sets of the Euclidean space, e.g. any self similar Delone set is linearly repetitive. We present here some combinatorial, ergodic and mixing properties of their associated dynamical systems. We also give a characterization of such sets via the patch frequencies. Finally, we explain why a linearly repetitive Delone set is the image of a lattice by a bi-Lipschitz map.

Original languageEnglish
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Pages195-222
Number of pages28
DOIs
Publication statusPublished - 2015

Publication series

NameProgress in Mathematics
Volume309
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

Keywords

  • Delone sets
  • Linearly repetitive
  • Tiling systems
  • Voronoï cell

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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