Number of bounded distance equivalence classes in hulls of repetitive Delone sets

Dirk Frettlöh; Alexey Garber; Lorenzo Sadun

doi:10.3934/dcds.2021157

Article Contents

2022, Volume 42, Issue 3: 1403-1414. Doi: 10.3934/dcds.2021157

This issue Previous Article Elliptic systems involving Schrödinger operators with vanishing potentials Next Article Lower bounds for Orlicz eigenvalues

Number of bounded distance equivalence classes in hulls of repetitive Delone sets

1.
Technische Fakultät, Bielefeld University, Postfach 100131, 33501 Bielefeld, Germany
2.
School of Mathematical & Statistical Sciences, The University of Texas Rio Grande Valley, 1 West University Blvd., Brownsville, TX 78520, USA
3.
Department of Mathematics, University of Texas, 2515 Speedway, PMA 8.100, Austin, TX 78712, USA

^* Corresponding author: Alexey Garber
^* Corresponding author: Alexey Garber

Received: February 2021

Revised: September 2021

Early access: November 2021

Published: March 2022

A.G. is partially supported by the Alexander von Humboldt Foundation.

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Abstract

Two Delone sets are bounded distance equivalent to each other if there is a bijection between them such that the distance of corresponding points is uniformly bounded. Bounded distance equivalence is an equivalence relation. We show that the hull of a repetitive Delone set with finite local complexity has either one equivalence class or uncountably many.

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Mathematics Subject Classification: Primary: 37B51, 52C23.

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References

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