Cantor subsystems on the Gehman dendrite
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929599162613760 |
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| author | Oprocha, Piotr Tomaszewski, Jakub |
| author_facet | Oprocha, Piotr Tomaszewski, Jakub |
| contents | In the present note we focus on dynamics on the Gehman dendrite $\mathcal{G}$. It is well-known that the set of its endpoints is homeomorphic to a standard Cantor ternary set. For any given surjective Cantor system $\mathcal{C}$ we provide constructions of (i) a mixing but not exact and (ii) an exact map on $\mathcal{G}$, such that in both cases the subsystem formed by $\text{End}(\mathcal{G})$ is conjugate to the initially chosen system on $\mathcal{C}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13336 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cantor subsystems on the Gehman dendrite Oprocha, Piotr Tomaszewski, Jakub Dynamical Systems In the present note we focus on dynamics on the Gehman dendrite $\mathcal{G}$. It is well-known that the set of its endpoints is homeomorphic to a standard Cantor ternary set. For any given surjective Cantor system $\mathcal{C}$ we provide constructions of (i) a mixing but not exact and (ii) an exact map on $\mathcal{G}$, such that in both cases the subsystem formed by $\text{End}(\mathcal{G})$ is conjugate to the initially chosen system on $\mathcal{C}$. |
| title | Cantor subsystems on the Gehman dendrite |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2411.13336 |