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arXiv · 2401.06314

$p$-adic rational maps having empty Fatou set

Aihua Fan·Shilei Fan·Yahia Mwanis·Yuefei Wang
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Abstract

On any finite algebraic extension $K$ of the field $\Q_p$ of $p$-adic numbers, there exist rational maps $\phi\in K(z)$ such that dynamical system $(\mathbb{P}^{1}(K),\phi)$ has empty Fatou set, i.e. the iteration family $\{\phi^n: n\geq 0\}$ is nowhere equicontinuous.

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Aihua Fan, Shilei Fan, Yahia Mwanis, Yuefei Wang. 2024-01-12. $p$-adic rational maps having empty Fatou set. https://arxiv.org/abs/2401.06314

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