Wandering domains for non-archimedean quadratic rational functions

Abstract

Let ${\mathbb{C}}_K$ be a complete and algebraic closed non-archimedean field with residual characteristic $2$. In this paper we prove that there exist $a,b\in {\mathbb{C}}_K$ such that the rational function $R(z)=\frac{z^2-z}{bz-\frac{1}{a}}$ has wandering components in its Fatou set.

arXiv comment18 pages