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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.08512 |
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| _version_ | 1866917003613175808 |
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| author | Epperlein, Jeremias |
| author_facet | Epperlein, Jeremias |
| contents | The action of a finite group $G$ on a subshift of finite type $X$ is called free, if every point has trivial stabilizer, and it is called inert, if the induced action on the dimension group of $X$ is trivial. We show that any two free inert actions of a finite group $G$ on an SFT are conjugate by an automorphism of any sufficiently high power of the shift space. This partially answers a question posed by Fiebig. As a consequence we obtain that every two free elements of the stabilized automorphism group of a full shift are conjugate in this group. In addition, we generalize a result of Boyle, Carlsen and Eilers concerning the flow equivalence of $G$-SFTs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08512 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Eventual Conjugacy of Free Inert $G$-SFTs Epperlein, Jeremias Dynamical Systems 37B10 (Primary) 37B15 (Secondary) The action of a finite group $G$ on a subshift of finite type $X$ is called free, if every point has trivial stabilizer, and it is called inert, if the induced action on the dimension group of $X$ is trivial. We show that any two free inert actions of a finite group $G$ on an SFT are conjugate by an automorphism of any sufficiently high power of the shift space. This partially answers a question posed by Fiebig. As a consequence we obtain that every two free elements of the stabilized automorphism group of a full shift are conjugate in this group. In addition, we generalize a result of Boyle, Carlsen and Eilers concerning the flow equivalence of $G$-SFTs. |
| title | Eventual Conjugacy of Free Inert $G$-SFTs |
| topic | Dynamical Systems 37B10 (Primary) 37B15 (Secondary) |
| url | https://arxiv.org/abs/2309.08512 |