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Orbit separation dimension as complexity measure for primitive inflation tilings

Baake, Michael ; Gahler, Franz and Gohlke, Philipp LU (2025) In Ergodic Theory and Dynamical Systems 45(10). p.2992-3020
Abstract

Orbit separation dimension , 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, thus providing a rich class of examples with non-trivial.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
complexity, inflation tilings, invariants, topological dynamics
in
Ergodic Theory and Dynamical Systems
volume
45
issue
10
pages
29 pages
publisher
Cambridge University Press
external identifiers
  • scopus:105005061293
ISSN
0143-3857
DOI
10.1017/etds.2025.18
language
English
LU publication?
yes
id
b6dfb740-7e92-4d2a-a5bc-3f9a4e150219
date added to LUP
2025-09-16 10:24:27
date last changed
2025-09-16 10:24:57
@article{b6dfb740-7e92-4d2a-a5bc-3f9a4e150219,
  abstract     = {{<p>Orbit separation dimension , 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, thus providing a rich class of examples with non-trivial.</p>}},
  author       = {{Baake, Michael and Gahler, Franz and Gohlke, Philipp}},
  issn         = {{0143-3857}},
  keywords     = {{complexity; inflation tilings; invariants; topological dynamics}},
  language     = {{eng}},
  number       = {{10}},
  pages        = {{2992--3020}},
  publisher    = {{Cambridge University Press}},
  series       = {{Ergodic Theory and Dynamical Systems}},
  title        = {{Orbit separation dimension as complexity measure for primitive inflation tilings}},
  url          = {{http://dx.doi.org/10.1017/etds.2025.18}},
  doi          = {{10.1017/etds.2025.18}},
  volume       = {{45}},
  year         = {{2025}},
}