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Singularities of inner functions associated with hyperbolic maps

Evdoridou, Vasiliki; Fagella, Núria; Jarque, Xavier and Sixsmith, David J. (2019). Singularities of inner functions associated with hyperbolic maps. Journal of Mathematical Analysis and Applications, 477(1) pp. 536–550.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1016/j.jmaa.2019.04.045
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Abstract

Let f be a function in the Eremenko-Lyubich class , and let U be an unbounded, forward invariant Fatou component of f. We relate the number of singularities of an inner function associated to with the number of tracts of f. In particular, we show that if f lies in either of two large classes of functions in , 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: Journal Item
Copyright Holders: 2019 Elsevier
ISSN: 0022-247X
Keywords: Transcendental dynamics; Inner functions; Hyperbolic functions.
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Related URLs:
Item ID: 60901
Depositing User: ORO Import
Date Deposited: 03 May 2019 09:22
Last Modified: 12 Jun 2019 16:47
URI: http://oro.open.ac.uk/id/eprint/60901
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