$p$-adic rational maps having empty Fatou set

On any finite algebraic extension $K$ of the field ${\text{Q}}_p$ 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 $\{{\phi }^n:n\ge 0\}$ is nowhere equicontinuous.