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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2501.05801 |
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| _version_ | 1866915820674744320 |
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| author | Jelić, Domagoj Oprocha, Piotr |
| author_facet | Jelić, Domagoj Oprocha, Piotr |
| contents | We show that if $G$ is a topological graph, and $f$ is continuous map, then the induced map $\tilde{f}$ acting on the hyperspace $C(G)$ of all connected subsets of $G$ by natural formula $\tilde{f}(C)=f(C)$ carries the same entropy as $f$.
This is well known that it does not hold on the larger hyperspace of all compact subsets. Also negative examples were given for the hyperspace $C(X)$ on some continua $X$, including dendrites.
Our work extends previous positive results obtained first for much simpler case of compact interval by completely different tools. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05801 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On recurrence and entropy in hyperspace of continua in dimension one Jelić, Domagoj Oprocha, Piotr Dynamical Systems 37E25, 54F16 We show that if $G$ is a topological graph, and $f$ is continuous map, then the induced map $\tilde{f}$ acting on the hyperspace $C(G)$ of all connected subsets of $G$ by natural formula $\tilde{f}(C)=f(C)$ carries the same entropy as $f$. This is well known that it does not hold on the larger hyperspace of all compact subsets. Also negative examples were given for the hyperspace $C(X)$ on some continua $X$, including dendrites. Our work extends previous positive results obtained first for much simpler case of compact interval by completely different tools. |
| title | On recurrence and entropy in hyperspace of continua in dimension one |
| topic | Dynamical Systems 37E25, 54F16 |
| url | https://arxiv.org/abs/2501.05801 |