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http://hdl.handle.net/2445/164100
Title: | Singular values and bounded Siegel disks |
Author: | Benini, Anna Miriam Fagella Rabionet, Núria |
Keywords: | Funcions meromorfes Sistemes dinàmics complexos Meromorphic functions Complex dynamical systems |
Issue Date: | 1-Sep-2018 |
Publisher: | Cambridge University Press |
Abstract: | Let $f$ be an entire transcendental function of finite order and $\Delta$ be a forward invariant bounded Siegel disk for $f$ with rotation number in Herman's class . We show that if $f$ has two singular values with bounded orbit, then the boundary of $\Delta$ contains a critical point. We also give a criterion under which the critical point in question is recurrent. We actually prove a more general theorem with less restrictive hypotheses, from which these results follow. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1017/S0305004117000469 |
It is part of: | Mathematical Proceedings of the Cambridge Philosophical Society, 2018, vol. 165, num. 2, p. 249-265 |
URI: | http://hdl.handle.net/2445/164100 |
Related resource: | https://doi.org/10.1017/S0305004117000469 |
ISSN: | 0305-0041 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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