Rigidity and Toeplitz systems
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917909951938560 |
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| author | Bruin, Henk Karpel, Olena Oprocha, Piotr Radinger, Silvia |
| author_facet | Bruin, Henk Karpel, Olena Oprocha, Piotr Radinger, Silvia |
| contents | The aim of this paper is to study measure-theoretical rigidity and partial rigidity for classes of Cantor dynamical systems including Toeplitz systems and enumeration systems. We use Bratteli diagrams to control invariant measures that are produced in our constructions. This leads to systems with desired properties. Among other things, we show that there exist Toeplitz systems with zero entropy which are not partially measure-theoretically rigid with respect to any of its invariant measures. We investigate enumeration systems defined by a linear recursion, prove that all such systems are partially rigid and present an example of an enumeration system which is not measure-theoretically rigid. We construct a minimal $\mathcal{S}$-adic Toeplitz subshift which has countably infinitely many ergodic invariant probability measures which are rigid for the same rigidity sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00917 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity and Toeplitz systems Bruin, Henk Karpel, Olena Oprocha, Piotr Radinger, Silvia Dynamical Systems 37B20 (Primary) 37B10, 37A05 (Secondary) The aim of this paper is to study measure-theoretical rigidity and partial rigidity for classes of Cantor dynamical systems including Toeplitz systems and enumeration systems. We use Bratteli diagrams to control invariant measures that are produced in our constructions. This leads to systems with desired properties. Among other things, we show that there exist Toeplitz systems with zero entropy which are not partially measure-theoretically rigid with respect to any of its invariant measures. We investigate enumeration systems defined by a linear recursion, prove that all such systems are partially rigid and present an example of an enumeration system which is not measure-theoretically rigid. We construct a minimal $\mathcal{S}$-adic Toeplitz subshift which has countably infinitely many ergodic invariant probability measures which are rigid for the same rigidity sequence. |
| title | Rigidity and Toeplitz systems |
| topic | Dynamical Systems 37B20 (Primary) 37B10, 37A05 (Secondary) |
| url | https://arxiv.org/abs/2502.00917 |