Orbit separation dimension as complexity measure for primitive inflation tilings
Dynamical Systems
2025-09-10 v2
Abstract
Orbit separation dimension (OSD), previously introduced as amorphic complexity, is a powerful complexity measure for topological dynamical systems with pure-point spectrum. Here, we develop methods and tools for it that allow a systematic application to translation dynamical systems of tiling spaces that are generated by primitive inflation rules. These systems share many nice properties that permit the explicit computation of the OSD, thus providing a rich class of examples with non-trivial OSD.
Keywords
Cite
@article{arxiv.2311.03541,
title = {Orbit separation dimension as complexity measure for primitive inflation tilings},
author = {Michael Baake and Franz Gähler and Philipp Gohlke},
journal= {arXiv preprint arXiv:2311.03541},
year = {2025}
}
Comments
29 pages, 1 figure, minor revisions and updates