Simultaneous Approximation by Attracting Basins
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918493962633216 |
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| author | Fisher, Colton Hill, Aiden Lazebnik, Kirill Thompson, Palmer |
| author_facet | Fisher, Colton Hill, Aiden Lazebnik, Kirill Thompson, Palmer |
| contents | We show that any $d\geq3$ pairwise-disjoint open sets $A_1$, ..., $A_d\subset\widehat{\mathbb{C}}$ sharing a common boundary $J$ can be simultaneously approximated by the $d$ attracting basins $\mathcal{A}_1$, ..., $\mathcal{A}_d$ of a rational map $r$ having Fatou set $\mathcal{F}(r)=\mathcal{A}_1\sqcup...\sqcup\mathcal{A}_d$ and so that the Julia set $\mathcal{J}(r)$ approximates $J$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09903 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Simultaneous Approximation by Attracting Basins Fisher, Colton Hill, Aiden Lazebnik, Kirill Thompson, Palmer Dynamical Systems Complex Variables 37F10 We show that any $d\geq3$ pairwise-disjoint open sets $A_1$, ..., $A_d\subset\widehat{\mathbb{C}}$ sharing a common boundary $J$ can be simultaneously approximated by the $d$ attracting basins $\mathcal{A}_1$, ..., $\mathcal{A}_d$ of a rational map $r$ having Fatou set $\mathcal{F}(r)=\mathcal{A}_1\sqcup...\sqcup\mathcal{A}_d$ and so that the Julia set $\mathcal{J}(r)$ approximates $J$. |
| title | Simultaneous Approximation by Attracting Basins |
| topic | Dynamical Systems Complex Variables 37F10 |
| url | https://arxiv.org/abs/2605.09903 |