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Orbit separation dimension as complexity measure for primitive inflation tilings
- Part of
-
- Journal:
- Ergodic Theory and Dynamical Systems / Volume 45 / Issue 10 / October 2025
- Published online by Cambridge University Press:
- 13 May 2025, pp. 2992-3020
- Print publication:
- October 2025
-
- Article
- Export citation
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Orbit separation dimension (
$\mathrm {OSD}$), 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 
$\mathrm {OSD}$, thus providing a rich class of examples with non-trivial 
$\mathrm {OSD}$.
