On the stability and shadowing of tree-shifts of finite type
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913257155985408 |
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| author | Bucki, Dawid |
| author_facet | Bucki, Dawid |
| contents | We investigate relations between the pseudo-orbit-tracing property, topological stability and openness for tree-shifts. We prove that a tree-shift is of finite type if and only if it has the pseudo-orbit-tracing property which implies that the tree-shift is topologically stable and all shift maps are open. We also present an example of a tree-shift for which all shift maps are open but which is not of finite type. It also turns out, that if a topologically stable tree-shift does not have isolated points then it is of finite type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04456 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the stability and shadowing of tree-shifts of finite type Bucki, Dawid Dynamical Systems 37B10, 37B51 (Primary) 37B25, 37B65 (Secondary) We investigate relations between the pseudo-orbit-tracing property, topological stability and openness for tree-shifts. We prove that a tree-shift is of finite type if and only if it has the pseudo-orbit-tracing property which implies that the tree-shift is topologically stable and all shift maps are open. We also present an example of a tree-shift for which all shift maps are open but which is not of finite type. It also turns out, that if a topologically stable tree-shift does not have isolated points then it is of finite type. |
| title | On the stability and shadowing of tree-shifts of finite type |
| topic | Dynamical Systems 37B10, 37B51 (Primary) 37B25, 37B65 (Secondary) |
| url | https://arxiv.org/abs/2403.04456 |