Expanding property and statistical laws for $p$-adic subhyperbolic rational maps
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866911756124684288 |
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| author | Fan, Shilei Liao, Lingmin Nie, Hongming Wang, Yuefei |
| author_facet | Fan, Shilei Liao, Lingmin Nie, Hongming Wang, Yuefei |
| contents | Let $K$ be a finite extension of the field $\mathbb{Q}_p$ of $p$-adic numbers. A rational map $ϕ\in K(z)$ of degree at least $2$ is subhyperbolic if each critical point in the $\mathbb{C}_p$-Julia set of $ϕ$ is eventually periodic. We show that subhyperbolic maps in $K(z)$ exhibit expanding property with respect to some (singular) metric. As an application, under a mild assumption, we establish several statistical laws for such maps in $K(z)$ with compact $\mathbb{C}_p$-Julia sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06322 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Expanding property and statistical laws for $p$-adic subhyperbolic rational maps Fan, Shilei Liao, Lingmin Nie, Hongming Wang, Yuefei Dynamical Systems 37P05 Let $K$ be a finite extension of the field $\mathbb{Q}_p$ of $p$-adic numbers. A rational map $ϕ\in K(z)$ of degree at least $2$ is subhyperbolic if each critical point in the $\mathbb{C}_p$-Julia set of $ϕ$ is eventually periodic. We show that subhyperbolic maps in $K(z)$ exhibit expanding property with respect to some (singular) metric. As an application, under a mild assumption, we establish several statistical laws for such maps in $K(z)$ with compact $\mathbb{C}_p$-Julia sets. |
| title | Expanding property and statistical laws for $p$-adic subhyperbolic rational maps |
| topic | Dynamical Systems 37P05 |
| url | https://arxiv.org/abs/2401.06322 |