On limit sets and equicontinuity in the hyperspace of continua in dimension one
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915820425183232 |
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| author | Jelić, Domagoj Oprocha, Piotr |
| author_facet | Jelić, Domagoj Oprocha, Piotr |
| contents | The paper studies the structure of $ω$-limit sets of map $\tilde{f}$ induced on the hyperspace $C(G)$ of all connected compact sets, by
dynamical system $(G,f)$ acting on a topological graph $G$. In the case of the base space being a topological tree we additionally show that $\tilde{f}$ is always almost
equicontinuous and characterize its Birkhoff center. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23264 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On limit sets and equicontinuity in the hyperspace of continua in dimension one Jelić, Domagoj Oprocha, Piotr Dynamical Systems The paper studies the structure of $ω$-limit sets of map $\tilde{f}$ induced on the hyperspace $C(G)$ of all connected compact sets, by dynamical system $(G,f)$ acting on a topological graph $G$. In the case of the base space being a topological tree we additionally show that $\tilde{f}$ is always almost equicontinuous and characterize its Birkhoff center. |
| title | On limit sets and equicontinuity in the hyperspace of continua in dimension one |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2602.23264 |