Let K be a non-archimedean field with residue field k, and suppose that k isnot an algebraic extension of a finite field. We prove two results concerningwandering domains of rational functions f in K(z) and Rivera-Letelier's notionof nontrivial reduction. First, if f has nontrivial reduction, then assumingsome simple hypotheses, we show that the Fatou set of f has wanderingcomponents by any of the usual definitions of such components. Second, we showthat if k has characteristic zero and K is discretely valued, then the converseholds; that is, the existence of a wandering domain implies that some iteratehas nontrivial reduction in some coordinate.
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