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Title: Singularities of inner functions associated with hyperbolic maps
Author: Evdoridou, Vasiliki
Fagella Rabionet, Núria
Jarque i Ribera, Xavier
Sixsmith, David J.
Keywords: Funcions de variables complexes
Funcions meromorfes
Sistemes dinàmics complexos
Functions of complex variables
Meromorphic functions
Complex dynamical systems
Issue Date: 1-Sep-2019
Publisher: Elsevier
Abstract: Let $f$ be a function in the Eremenko-Lyubich class $\mathscr{B}$, and let $U$ be an unbounded, forward invariant Fatou component of $f$. We relate the number of singularities of an inner function associated to $\left.f\right|_{U}$ with the number of tracts of $f$. In particular, we show that if $f$ lies in either of two large classes of functions in $\mathscr{B}$, 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.
Note: Versió postprint del document publicat a:
It is part of: Journal of Mathematical Analysis and Applications, 2019, vol. 477, num. 1, p. 536-550
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ISSN: 0022-247X
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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