2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69418Let K be a non-archimedean field with residue field k, and suppose that k is not an algebraic extension of a finite field. We prove two results concerning wandering domains of rational functions f in K(z) and Rivera-Letelier's notion of nontrivial reduction. First, if f has nontrivial reduction, then assuming some simple hypotheses, we show that the Fatou set of f has wandering components by any of the usual definitions of such components. Second, we show that if k has characteristic zero and K is discretely valued, then the converse holds; that is, the existence of a wandering domain implies that some iterate has nontrivial reduction in some coordinate.22 pages; to appear in Ill. J. Math.; added appendix and some more examples; a few other minor changesNumber TheoryDynamical Systems11S80 (Primary) 37F10, 54H20 (Secondary)text