Julia and escaping set spiders' webs of positive area

Sixsmith, Dave (2015). Julia and escaping set spiders' webs of positive area. International Mathematics Research Notices, 2015(19) pp. 9751–9774.

DOI: https://doi.org/10.1093/imrn/rnu245

Abstract

We study the dynamics of a collection of families of transcendental entire functions which generalises the well-known exponential and cosine families. We show that for functions in many of these families the Julia set, the escaping set and the fast escaping set are all spiders' webs of positive area. This result is unusual in that most of these functions lie outside the Eremenko-Lyubich class Β. This is also the first result on the area of a spider's web.

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About

• Item ORO ID
• 41343
• Item Type
• Journal Item
• ISSN
• 1687-0247
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Dimensions in complex dynamics: spiders' webs and speed of escape	EP/J022160/1	EPSRC (Engineering and Physical Sciences Research Council)

• 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
• © 2014 The Authors
• Depositing User
• Dave Sixsmith