The iterated minimum modulus and conjectures of Baker and Eremenko

Osborne, John W.; Rippon, Philip J. and Stallard, Gwyneth M. (2019). The iterated minimum modulus and conjectures of Baker and Eremenko. Journal d’Analyse Mathematique, 139(2) pp. 521–558.

DOI: https://doi.org/10.1007/s11854-019-0065-z

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.

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About

• Item ORO ID
• 48913
• Item Type
• Journal Item
• ISSN
• 0021-7670
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Bakers Conjecture and Eremenko's Conjecture: New Directions (XM-12-066-GS)	EP/K031163/1	EPSRC (Engineering and Physical Sciences Research Council)

• Keywords
• transcendental entire function; minimum modulus; weak spider's web; escaping set; Baker domain
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM)
  Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
• Copyright Holders
• © 2019 Journal d'Analyse Mathematique
• Related URLs
• • https://arxiv.org/abs/1609.06644(Other)
• Depositing User
• Philip Rippon