$p$-adic rational maps having empty Fatou set
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929207554080768 |
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| author | Fan, Aihua Fan, Shilei Mwanis, Yahia Wang, Yuefei |
| author_facet | Fan, Aihua Fan, Shilei Mwanis, Yahia Wang, Yuefei |
| contents | On any finite algebraic extension $K$ of the field $\Q_p$ of $p$-adic numbers, there exist rational maps $ϕ\in K(z)$ such that dynamical system $(\mathbb{P}^{1}(K),ϕ)$ has empty Fatou set, i.e. the iteration family $\{ϕ^n: n\geq 0\}$ is nowhere equicontinuous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06314 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $p$-adic rational maps having empty Fatou set Fan, Aihua Fan, Shilei Mwanis, Yahia Wang, Yuefei Dynamical Systems Primary 37P05, Secondary 11S82, 37B05 On any finite algebraic extension $K$ of the field $\Q_p$ of $p$-adic numbers, there exist rational maps $ϕ\in K(z)$ such that dynamical system $(\mathbb{P}^{1}(K),ϕ)$ has empty Fatou set, i.e. the iteration family $\{ϕ^n: n\geq 0\}$ is nowhere equicontinuous. |
| title | $p$-adic rational maps having empty Fatou set |
| topic | Dynamical Systems Primary 37P05, Secondary 11S82, 37B05 |
| url | https://arxiv.org/abs/2401.06314 |