Permutable entire functions and multiply connected wandering domains

Benini, Anna Miriam; Rippon, Philip J. and Stallard, Gwyneth M. (2016). Permutable entire functions and multiply connected wandering domains. Advances in Mathematics, 287 pp. 451–462.

DOI: https://doi.org/10.1016/j.aim.2015.04.031

Abstract

Let f and g be permutable transcendental entire functions. We use a recent analysis of the dynamical behaviour in multiply connected wandering domains to make progress on the long standing conjecture that the Julia sets of f and g are equal; in particular, we show that J(f)=J(g) provided that neither f nor g has a simply connected wandering domain in the fast escaping set.

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI

About

• Item ORO ID
• 44549
• Item Type
• Journal Item
• ISSN
• 1090-2082
• 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; Julia set; permutable functions; multiply connected wandering domain; fast escaping set
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2015 Elsevier Inc.
• Depositing User
• Philip Rippon