Dynamical Invariants from Asymptotic Composants
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910028786565120 |
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| author | Gähler, Franz |
| author_facet | Gähler, Franz |
| contents | Asymptotic composants and their incidence relations are powerful invariants of 1-dimensional inflation tilings spaces, which can distinguish many MLD classes of tilings. In particular, and unlike most other invariants, they can often provide obstructions to a tiling space being MLD to its reflection. We present a simple algorithm to determine these asymptotic composants for primitive inflation tiling spaces in one dimension, and illustrate how they can be used to tell different MLD classes of tilings apart. In an Appendix, we then show that the structure of asymptotic composants, together with the orbit separation dimension (OSD), can distinguish all MLD classes of inflations tilings with pure-point spectrum for a bunch of small inflation factors, which illustrates the power of these invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18501 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dynamical Invariants from Asymptotic Composants Gähler, Franz Dynamical Systems General Relativity and Quantum Cosmology 37B52 (Primary) 52C23 (Secondary) Asymptotic composants and their incidence relations are powerful invariants of 1-dimensional inflation tilings spaces, which can distinguish many MLD classes of tilings. In particular, and unlike most other invariants, they can often provide obstructions to a tiling space being MLD to its reflection. We present a simple algorithm to determine these asymptotic composants for primitive inflation tiling spaces in one dimension, and illustrate how they can be used to tell different MLD classes of tilings apart. In an Appendix, we then show that the structure of asymptotic composants, together with the orbit separation dimension (OSD), can distinguish all MLD classes of inflations tilings with pure-point spectrum for a bunch of small inflation factors, which illustrates the power of these invariants. |
| title | Dynamical Invariants from Asymptotic Composants |
| topic | Dynamical Systems General Relativity and Quantum Cosmology 37B52 (Primary) 52C23 (Secondary) |
| url | https://arxiv.org/abs/2602.18501 |