Wandering domains for non-archimedean quadratic rational functions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916218532790272 |
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| author | Nopal-Coello, Víctor |
| author_facet | Nopal-Coello, Víctor |
| contents | Let $\mathbb{C}_K$ be a complete and algebraic closed non-archimedean field with residual characteristic $2$. In this paper we prove that there exist $a,b\in\mathbb{C}_K$ such that the rational function $R(z)=\frac{z^2-z}{bz-\frac{1}{a}}$ has wandering components in its Fatou set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14614 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wandering domains for non-archimedean quadratic rational functions Nopal-Coello, Víctor Dynamical Systems 37P05, 37P40, 11S82 Let $\mathbb{C}_K$ be a complete and algebraic closed non-archimedean field with residual characteristic $2$. In this paper we prove that there exist $a,b\in\mathbb{C}_K$ such that the rational function $R(z)=\frac{z^2-z}{bz-\frac{1}{a}}$ has wandering components in its Fatou set. |
| title | Wandering domains for non-archimedean quadratic rational functions |
| topic | Dynamical Systems 37P05, 37P40, 11S82 |
| url | https://arxiv.org/abs/2404.14614 |