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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:
It is part of: Mathematical Proceedings of the Cambridge Philosophical Society, 2018, vol. 165, num. 2, p. 249-265
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ISSN: 0305-0041
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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