Wandering domains and nontrivial reduction in non-archimedean dynamics

dc.creatorBenedetto, Robert L.
dc.date2003-12-01
dc.date2004-12-06
dc.date.accessioned2026-07-07T05:03:26Z
dc.date.available2026-07-07T05:03:26Z
dc.descriptionLet 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.
dc.description22 pages; to appear in Ill. J. Math.; added appendix and some more examples; a few other minor changes
dc.identifierhttps://arxiv.org/abs/math/0312034
dc.identifierhttp://arxiv.org/abs/math/0312034
dc.identifierIll. J. Math. 49 (2005), no. 1, pp. 167--193
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69418
dc.subjectNumber Theory
dc.subjectDynamical Systems
dc.subject11S80 (Primary) 37F10, 54H20 (Secondary)
dc.titleWandering domains and nontrivial reduction in non-archimedean dynamics
dc.typetext

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