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http://hdl.handle.net/2445/164098
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: 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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