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

In this paper we study dynamics on the Fatou set of a rational function φ ∈ $\overline {\Bbb{Q}}_p(z)$ . 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.

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