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The iterated minimum modulus and conjectures of Baker and Eremenko

Osborne, John; Rippon, Philip and Stallard, Gwyneth (2020). The iterated minimum modulus and conjectures of Baker and Eremenko. Journal d’Analyse Mathematique (In Press).

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Abstract

In transcendental dynamics significant progress has been made by studying points whose iterates escape to infinity at least as fast as iterates of the maximum modulus. Here we take the novel approach of studying points whose iterates escape at least as fast as iterates of the minimum modulus, and obtain new results related to Eremenko's conjecture and Baker's conjecture, and the rate of escape in Baker domains. To do this we prove a result of wider interest concerning the existence of points that escape to infinity under the iteration of a positive continuous function.

Item Type: Journal Item
Copyright Holders: Journal d'Analyse Mathematique
ISSN: 0021-7670
Project Funding Details:
Funded Project NameProject IDFunding Body
Bakers Conjecture and Eremenko's Conjecture: New Directions (XM-12-066-GS)EP/K031163/1EPSRC (Engineering and Physical Sciences Research Council)
Keywords: transcendental entire function; minimum modulus; weak spider's web; escaping set; Baker domain
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM)
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Related URLs:
Item ID: 48913
Depositing User: Philip Rippon
Date Deposited: 13 Mar 2017 14:39
Last Modified: 24 Mar 2017 10:44
URI: http://oro.open.ac.uk/id/eprint/48913
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