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Escaping points of entire functions of small growth

Rippon, P. J. and Stallard, G. M. (2009). Escaping points of entire functions of small growth. Mathematische Zeitschrift, 261(3) pp. 557–570.

DOI (Digital Object Identifier) Link: https://doi.org/10.1007/s00209-008-0339-0
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Abstract

Let f be a transcendental entire function and let I(f) denote the set of points that escape to infinity under iteration. We give conditions which ensure that, for certain functions, I(f) is connected. In particular, we show that I(f) is connected if f has order zero and sufficiently small growth or has order less than 1/2 and regular growth. This shows that, for these functions, Eremenko’s conjecture that I(f) has no bounded components is true. We also give a new criterion related to I(f) which is sufficient to ensure that f has no unbounded Fatou components.

Item Type: Journal Item
Copyright Holders: 2008 Springer-Verlag
ISSN: 0025-5874
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 18351
Depositing User: Colin Smith
Date Deposited: 08 Sep 2009 09:34
Last Modified: 04 Oct 2016 10:27
URI: http://oro.open.ac.uk/id/eprint/18351
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