P-Adic Dynamics and Sullivan's No Wandering Domains Theorem

Abstract

In this paper we study dynamics on the Fatou set of a rational function φ ∈ . Using a notion of ‘components’ of the Fatou set defined by Benedetto, we state and prove an analogue of Sullivan's No Wandering Domains Theorem for p-adic rational functions which have no wild recurrent Julia critical points.