Yahia Mwanis

$p$-adic rational maps having empty Fatou set

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