Lelek-like Fans: Endpoint-dense Continua Supporting Topologically Mixing Maps
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913823966887936 |
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| author | Banic, Iztok Erceg, Goran Jelic, Ivan Kennedy, Judy |
| author_facet | Banic, Iztok Erceg, Goran Jelic, Ivan Kennedy, Judy |
| contents | The Lelek fan is the only smooth fan that has a dense set of end-points. In this paper, we study non-smooth fans with this property; i.e., we construct an uncountable family of pairwise non-homeomorphic such fans. Furthermore, we prove that each of them admits a topologically mixing non-invertible mapping as well as a topologically mixing homeomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03933 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lelek-like Fans: Endpoint-dense Continua Supporting Topologically Mixing Maps Banic, Iztok Erceg, Goran Jelic, Ivan Kennedy, Judy Dynamical Systems The Lelek fan is the only smooth fan that has a dense set of end-points. In this paper, we study non-smooth fans with this property; i.e., we construct an uncountable family of pairwise non-homeomorphic such fans. Furthermore, we prove that each of them admits a topologically mixing non-invertible mapping as well as a topologically mixing homeomorphism. |
| title | Lelek-like Fans: Endpoint-dense Continua Supporting Topologically Mixing Maps |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2505.03933 |