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arXiv · 2401.06322

Expanding property and statistical laws for $p$-adic subhyperbolic rational maps

Shilei Fan·Lingmin Liao·Hongming Nie·Yuefei Wang
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Abstract

Let $K$ be a finite extension of the field $\mathbb{Q}_p$ of $p$-adic numbers. A rational map $\phi\in K(z)$ of degree at least $2$ is subhyperbolic if each critical point in the $\mathbb{C}_p$-Julia set of $\phi$ 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.

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Shilei Fan, Lingmin Liao, Hongming Nie, Yuefei Wang. 2024-01-12. Expanding property and statistical laws for $p$-adic subhyperbolic rational maps. https://arxiv.org/abs/2401.06322

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