Dynamic rays of bounded-type transcendental self-maps of the punctured plane
Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
Martí-Pete, David (Open University. School of Mathematics and Statistics (UK))

Date:	2017
Abstract:	We study the escaping set of functions in the class B∗, that is, transcendental self-maps of ℂ∗ for which the set of singular values is contained in a compact annulus of ℂ∗ that separates zero from infinity. For functions in the class B∗, escaping points lie in their Julia set. If f is a composition of finite order transcendental self-maps of ℂ∗ (and hence, in the class B∗), then we show that every escaping point of f can be connected to one of the essential singularities by a curve of points that escape uniformly. Moreover, for every sequence e ∈ {0,∞}, we show that the escaping set of f contains a Cantor bouquet of curves that accumulate to the set {0,∞} according to e under iteration by f.
Grants:	Ministerio de Economía y Competitividad MTM2011-26995-C02-02 Ministerio de Economía y Competitividad MTM2014-52209-C2-2-P
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Complex dynamics ; Transcendental functions ; Punctured plane ; Escaping set ; Dynamic rays ; Bounded-type functions
Published in:	Discrete and continuous dynamical systems. Series A, Vol. 37, Issue 6 (June 2017) , p. 3123-3160, ISSN 1553-5231

DOI: 10.3934/dcds.2017134

Postprint 40 p, 10.0 MB

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