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

Authors

Dirk Frettlöh
Alexey Garber, The University of Texas Rio Grande Valley
Lorenzo Sadun

Document Type

Article

Publication Date

3-2022

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.

Recommended Citation

Frettlöh, D., Garber, A., & Sadun, L. (2022). Number of bounded distance equivalence classes in hulls of repetitive Delone sets. Discrete & Continuous Dynamical Systems, 42(3), 1403. https://doi.org/10.3934/dcds.2021157

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Discrete & Continuous Dynamical Systems

DOI

10.3934/dcds.2021157