Julia sets and geometrically finite maps over finite extensions of the $p$-adic field

Shilei Fan, Lingmin Liao, Hongmin Nie +1

Let $K$ be a finite extension of the field ${\mathbb{Q}}_p$ of $p$-adic numbers, and $\varphi \in K(z)$ be a rational map of degree at least $2$. We prove that the $K$-Julia set of $\varphi$ is t…