Tranched graphs: consequences for topology and dynamics
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918509611581440 |
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| author | Kowalewski, Michał Oprocha, Piotr |
| author_facet | Kowalewski, Michał Oprocha, Piotr |
| contents | We compare quasi-graphs and generalized $\sin(1/x)$-type continua, which are two classes of continua that generalize topological graphs and contain the Warsaw circle as a nontrivial common element. We show that neither class is a subset of the other, provide some characterizations, and present illustrative examples. We unify both approaches by considering the class of tranched graphs, compare it to concepts known from the literature, and describe how the topological structure of its elements restricts possible dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05407 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tranched graphs: consequences for topology and dynamics Kowalewski, Michał Oprocha, Piotr General Topology Dynamical Systems 54E45, 54F15, 37B45 (Primary) 54G15, 37B02 (Secondary) We compare quasi-graphs and generalized $\sin(1/x)$-type continua, which are two classes of continua that generalize topological graphs and contain the Warsaw circle as a nontrivial common element. We show that neither class is a subset of the other, provide some characterizations, and present illustrative examples. We unify both approaches by considering the class of tranched graphs, compare it to concepts known from the literature, and describe how the topological structure of its elements restricts possible dynamics. |
| title | Tranched graphs: consequences for topology and dynamics |
| topic | General Topology Dynamical Systems 54E45, 54F15, 37B45 (Primary) 54G15, 37B02 (Secondary) |
| url | https://arxiv.org/abs/2405.05407 |