Substitution tilings with transcendental inflation factor
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912111736651776 |
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| author | Frettlöh, Dirk Garber, Alexey Mañibo, Neil |
| author_facet | Frettlöh, Dirk Garber, Alexey Mañibo, Neil |
| contents | For any $λ>2$, we construct a substitution on an infinite alphabet which gives rise to a substitution tiling with inflation factor $λ$. In particular, we obtain the first class of examples of substitutive systems with transcendental inflation factors that possess usual dynamical properties enjoyed by primitive substitutions on finite alphabets. We show that both the associated subshift and tiling dynamical systems are strictly ergodic, which is related to the quasicompactness of the underlying substitution operator. We also provide an explicit substitution with transcendental inflation factor $λ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_01327 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Substitution tilings with transcendental inflation factor Frettlöh, Dirk Garber, Alexey Mañibo, Neil Dynamical Systems Metric Geometry 37B10, 47B65, 52C23, 05B45 For any $λ>2$, we construct a substitution on an infinite alphabet which gives rise to a substitution tiling with inflation factor $λ$. In particular, we obtain the first class of examples of substitutive systems with transcendental inflation factors that possess usual dynamical properties enjoyed by primitive substitutions on finite alphabets. We show that both the associated subshift and tiling dynamical systems are strictly ergodic, which is related to the quasicompactness of the underlying substitution operator. We also provide an explicit substitution with transcendental inflation factor $λ$. |
| title | Substitution tilings with transcendental inflation factor |
| topic | Dynamical Systems Metric Geometry 37B10, 47B65, 52C23, 05B45 |
| url | https://arxiv.org/abs/2208.01327 |