Relative topological entropy and relative mean dimension of induced factors
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918214933413888 |
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| author | Liu, Kairan Qiao, Yixiao |
| author_facet | Liu, Kairan Qiao, Yixiao |
| contents | We study the relation of relative topological entropy and relative mean dimension between a factor map and its induced factor map for amenable group actions. On the one hand, we prove that a factor map has zero relative topological entropy if and only if so does the induced factor map. On the other hand, we prove that a factor map has positive relative topological entropy if and only if the induced factor map has infinite relative mean dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18040 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relative topological entropy and relative mean dimension of induced factors Liu, Kairan Qiao, Yixiao Dynamical Systems We study the relation of relative topological entropy and relative mean dimension between a factor map and its induced factor map for amenable group actions. On the one hand, we prove that a factor map has zero relative topological entropy if and only if so does the induced factor map. On the other hand, we prove that a factor map has positive relative topological entropy if and only if the induced factor map has infinite relative mean dimension. |
| title | Relative topological entropy and relative mean dimension of induced factors |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2511.18040 |