Amorphic complexity and entropy for symbolic model sets

TL;DR

This paper investigates the relationship between amorphic complexity and entropy in symbolic model sets, providing continuity results and constructing subshifts with diverse dynamical behaviors.

Contribution

It introduces a continuity result for the Weyl pseudometric on model set subshifts and explores their entropy and amorphic complexity properties.

Findings

Continuity of the Weyl pseudometric on subshifts generated by model sets.

Construction of subshifts with varying entropy and amorphic complexity.

Analysis of the maximal equicontinuous factor in these subshifts.

Abstract

We show a continuity result for the Weyl pseudometric on subshifts which are generated by model sets. This fact is then used for multiple constructions of subshifts that exhibit different behavior regarding entropy, amorphic complexity and their maximal equicontinuous factor.