Singularities of inner functions associated with hyperbolic maps
Evdoridou, Vasiliki (The Open University)
Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
Sixsmith, David J. (University of Liverpool)

Date:	2019
Abstract:	Let f be a function in the Eremenko-Lyubich class B, and let U be an unbounded, forward invariant Fatou component of f. We relate the number of singularities of an inner function associated to f $w ith the number of tracts of f. In particular, we show that if f lies in either of two large classes of functions in B, and also has finitely many tracts, then the number of singularities of an associated inner function is at most equal to the number of tracts of f. Our results imply that for hyperbolic functions of finite order there is an upper bound - related to the order - on the number of singularities of an associated inner function.
Grants:	Ministerio de Economía y Competitividad MTM2017-86795-C3-2-P Ministerio de Economía y Competitividad MDM-2014-0445 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1374
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Transcendental dynamics ; Inner functions ; Hyperbolic functions
Published in:	Journal of mathematical analysis and applications, Vol. 477, Issue 1 (September 2019) , p. 536-550, ISSN 1096-0813

DOI: 10.1016/j.jmaa.2019.04.045

Postprint 17 p, 411.0 KB

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