NUMBER OF BOUNDED DISTANCE EQUIVALENCE CLASSES IN HULLS OF REPETITIVE DELONE SETS

Dirk Frettlöh,Alexey Garber,Lorenzo Sadun

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS（2022）

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摘要

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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关键词

Delone set, finite local complexity, topological hull, bounded distance equivalence, aperiodic order, aperiodic tilings

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