Evdoridou, Vasiliki, Fagellab, Nuria, Jarque, Xavier and Sixsmith, David J ORCID: 0000-0002-3543-6969
(2019)
Singularities of inner functions associated with hyperbolic maps.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 477 (1).
pp. 536-550.
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Abstract
Let $f$ be a function in the Eremenko-Lyubich class $\mathcal{B}$, and let $U$ be an unbounded, forward invariant Fatou component of $f$. We relate the number of singularities of an inner function associated to $f|_U$ with the number of tracts of $f$. In particular, we show that if $f$ lies in either of two large classes of functions in $\mathcal{B}$, 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.
Item Type: | Article |
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Uncontrolled Keywords: | Transcendental dynamics, Inner functions, Hyperbolic functions |
Depositing User: | Symplectic Admin |
Date Deposited: | 17 Apr 2019 14:49 |
Last Modified: | 19 Jan 2023 00:54 |
DOI: | 10.1016/j.jmaa.2019.04.045 |
Related URLs: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3037292 |