Non-recurrent rational maps with disconnected Julia set
Fuente:
arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866916939795791872 |
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| author | Gao, Yan Xu, Lele Yang, Luxian |
| author_facet | Gao, Yan Xu, Lele Yang, Luxian |
| contents | We prove that every wandering exposed Julia component of a rational map is to a singleton, provided that each wandering Julia component containing critical points is non-recurrent. Moreover, we show that the Julia set contains only finitely many periodic complex-type components if each wandering Julia component containing critical values is non-recurrent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06645 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-recurrent rational maps with disconnected Julia set Gao, Yan Xu, Lele Yang, Luxian Dynamical Systems We prove that every wandering exposed Julia component of a rational map is to a singleton, provided that each wandering Julia component containing critical points is non-recurrent. Moreover, we show that the Julia set contains only finitely many periodic complex-type components if each wandering Julia component containing critical values is non-recurrent. |
| title | Non-recurrent rational maps with disconnected Julia set |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2509.06645 |