Hénon maps with many rational periodic points
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866915375231270912 |
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| author | Kim, Hyeonggeun Krieger, Holly Postolache, Mara-Ioana Szeto, Vivian |
| author_facet | Kim, Hyeonggeun Krieger, Holly Postolache, Mara-Ioana Szeto, Vivian |
| contents | Building on work of Doyle and Hyde on polynomial maps in one variable, we produce for each odd integer $d \geq 2$ a Hénon map of degree $d$ defined over $\mathbb{Q}$ with at least $(d-4)^2$ integral periodic points. This provides a quadratic lower bound on any conjectural uniform bound for periodic rational points of Hénon maps. In contrast with the work of Doyle and Hyde, our examples also admit integer cycles of large period. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01668 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hénon maps with many rational periodic points Kim, Hyeonggeun Krieger, Holly Postolache, Mara-Ioana Szeto, Vivian Dynamical Systems Number Theory Building on work of Doyle and Hyde on polynomial maps in one variable, we produce for each odd integer $d \geq 2$ a Hénon map of degree $d$ defined over $\mathbb{Q}$ with at least $(d-4)^2$ integral periodic points. This provides a quadratic lower bound on any conjectural uniform bound for periodic rational points of Hénon maps. In contrast with the work of Doyle and Hyde, our examples also admit integer cycles of large period. |
| title | Hénon maps with many rational periodic points |
| topic | Dynamical Systems Number Theory |
| url | https://arxiv.org/abs/2412.01668 |