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Spring 2005 Wandering domains and nontrivial reduction in non-Archimedean dynamics
Robert L. Benedetto
Illinois J. Math. 49(1): 167-193 (Spring 2005). DOI: 10.1215/ijm/1258138313

Abstract

Let $K$ 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 $\phi\in K(z)$ and Rivera-Letelier's notion of nontrivial reduction. First, if $\phi$ has nontrivial reduction, then assuming some simple hypotheses, we show that the Fatou set of $\phi$ has wandering components by any of the usual definitions of ``components of the Fatou set''. Second, we show that if $k$ has characteristic zero and $K$ is discretely valued, then the existence of a wandering domain implies that some iterate has nontrivial reduction in some coordinate.

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Robert L. Benedetto. "Wandering domains and nontrivial reduction in non-Archimedean dynamics." Illinois J. Math. 49 (1) 167 - 193, Spring 2005. https://doi.org/10.1215/ijm/1258138313

Information

Published: Spring 2005
First available in Project Euclid: 13 November 2009

zbMATH: 1137.11354
MathSciNet: MR2157374
Digital Object Identifier: 10.1215/ijm/1258138313

Subjects:
Primary: 11S85
Secondary: 37B99 , 37F10 , 37F50

Rights: Copyright © 2005 University of Illinois at Urbana-Champaign

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Vol.49 • No. 1 • Spring 2005
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