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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2305.00726 |
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| _version_ | 1866914639993896960 |
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| author | Codenotti, Alessandro |
| author_facet | Codenotti, Alessandro |
| contents | Glasner and Megrelishvili proved that every continuous action of a topological group $G$ on a dendrite $X$ is tame. We produce two examples of an action on a dendrite which is not $\mathrm{tame}_1$, answering a question they raised. We then show that actions on dendrites have $β$-rank at most $2$ and produce examples of tame metric dynamical systems of $β$-rank $α$ for any $α<ω_1$, answering another question of Glasner and Megrelishvili. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00726 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some examples of tame dynamical systems answering questions of Glasner and Megrelishvili Codenotti, Alessandro Dynamical Systems Glasner and Megrelishvili proved that every continuous action of a topological group $G$ on a dendrite $X$ is tame. We produce two examples of an action on a dendrite which is not $\mathrm{tame}_1$, answering a question they raised. We then show that actions on dendrites have $β$-rank at most $2$ and produce examples of tame metric dynamical systems of $β$-rank $α$ for any $α<ω_1$, answering another question of Glasner and Megrelishvili. |
| title | Some examples of tame dynamical systems answering questions of Glasner and Megrelishvili |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2305.00726 |