Orbit separation dimension as complexity measure for primitive inflation tilings
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916940767821824 |
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| author | Baake, Michael Gähler, Franz Gohlke, Philipp |
| author_facet | Baake, Michael Gähler, Franz Gohlke, Philipp |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03541 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Orbit separation dimension as complexity measure for primitive inflation tilings Baake, Michael Gähler, Franz Gohlke, Philipp Dynamical Systems 37B52, 52C23 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. |
| title | Orbit separation dimension as complexity measure for primitive inflation tilings |
| topic | Dynamical Systems 37B52, 52C23 |
| url | https://arxiv.org/abs/2311.03541 |