Locating critical points attracted to p-adic attracting cycles
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911382832676864 |
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| author | Rivera-Letelier, Juan |
| author_facet | Rivera-Letelier, Juan |
| contents | In complex dynamics, a fundamental result of Fatou and Julia asserts that every attracting cycle of a rational map attracts a critical point. The analogous statement fails in non-Archimedean dynamics. For a non-Archimedean rational map, this paper establishes a sharp condition on the multiplier of an attracting cycle ensuring it attracts a critical point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12163 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Locating critical points attracted to p-adic attracting cycles Rivera-Letelier, Juan Dynamical Systems Number Theory In complex dynamics, a fundamental result of Fatou and Julia asserts that every attracting cycle of a rational map attracts a critical point. The analogous statement fails in non-Archimedean dynamics. For a non-Archimedean rational map, this paper establishes a sharp condition on the multiplier of an attracting cycle ensuring it attracts a critical point. |
| title | Locating critical points attracted to p-adic attracting cycles |
| topic | Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/2601.12163 |