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Connectedness properties of the set where the iterates of an entire function are unbounded

Osborne, John; Rippon, Philip and Stallard, Gwyneth (2017). Connectedness properties of the set where the iterates of an entire function are unbounded. Ergodic Theory and Dynamical Systems, 37(4) pp. 1291–1307.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1017/etds.2015.85
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Abstract

We investigate the connectedness properties of the set I+(f) of points where the iterates of an entire function f are unbounded. In particular, we show that I+(f) is connected whenever iterates of the minimum modulus of f tend to ∞. For a general transcendental entire function f, we show that I+(f)∪ \{\infty\} is always connected and that, if I+(f) is disconnected, then it has uncountably many components, infinitely many of which are unbounded.

Item Type: Journal Item
Copyright Holders: 2016 Ergodic Theory and Dynamical Systems
ISSN: 1469-4417
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)
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: 44199
Depositing User: Philip Rippon
Date Deposited: 27 Aug 2015 08:44
Last Modified: 23 May 2019 20:31
URI: http://oro.open.ac.uk/id/eprint/44199
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