Linearly repetitive Delone systems have a finite number of non periodic Delone system factors

TL;DR

This paper proves that linearly repetitive Delone systems have only finitely many non-periodic factors up to conjugacy, which also applies to tiling systems, advancing understanding of their structural complexity.

Contribution

The paper establishes a finiteness result for factors of linearly repetitive Delone systems, a significant step in the study of their dynamical properties.

Findings

Finitely many non-periodic Delone system factors exist for linearly repetitive systems

The result extends to linearly repetitive tiling systems

Advances understanding of the structural complexity of Delone systems

Abstract

We prove linearly repetitive Delone systems have finitely many Delone system factors up to conjugacy. This result is also applicable to linearly repetitive tiling systems.