Evdoridou, VasilikiFagella Rabionet, NúriaJarque i Ribera, XavierSixsmith, David J.2020-06-032021-09-012019-09-010022-247Xhttps://hdl.handle.net/2445/164098Let $f$ 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.15 p.application/pdfengcc-by-nc-nd (c) Elsevier, 2019http://creativecommons.org/licenses/by-nc-nd/3.0/esFuncions de variables complexesFuncions meromorfesSistemes dinàmics complexosFunctions of complex variablesMeromorphic functionsComplex dynamical systemsinfo:eu-repo/semantics/article6835312020-06-03info:eu-repo/semantics/openAccess