Wandering domains and nontrivial reduction in non-archimedean dynamics
| dc.creator | Benedetto, Robert L. | |
| dc.date | 2003-12-01 | |
| dc.date | 2004-12-06 | |
| dc.date.accessioned | 2026-07-07T05:03:26Z | |
| dc.date.available | 2026-07-07T05:03:26Z | |
| dc.description | 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 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.description | 22 pages; to appear in Ill. J. Math.; added appendix and some more examples; a few other minor changes | |
| dc.identifier | https://arxiv.org/abs/math/0312034 | |
| dc.identifier | http://arxiv.org/abs/math/0312034 | |
| dc.identifier | Ill. J. Math. 49 (2005), no. 1, pp. 167--193 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69418 | |
| dc.subject | Number Theory | |
| dc.subject | Dynamical Systems | |
| dc.subject | 11S80 (Primary) 37F10, 54H20 (Secondary) | |
| dc.title | Wandering domains and nontrivial reduction in non-archimedean dynamics | |
| dc.type | text |