Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/164098
 Title: Singularities of inner functions associated with hyperbolic maps Author: Evdoridou, VasilikiFagella Rabionet, NúriaJarque i Ribera, XavierSixsmith, David J. Keywords: Funcions de variables complexesFuncions meromorfesSistemes dinàmics complexosFunctions of complex variablesMeromorphic functionsComplex 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: https://doi.org/10.1016/j.jmaa.2019.04.045 It is part of: Journal of Mathematical Analysis and Applications, 2019, vol. 477, num. 1, p. 536-550 URI: http://hdl.handle.net/2445/164098 Related resource: https://doi.org/10.1016/j.jmaa.2019.04.045 ISSN: 0022-247X Appears in Collections: Articles publicats en revistes (Matemàtiques i Informàtica)

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