Julia and escaping set spiders' webs of positive area


Sixsmith, DJ ORCID: 0000-0002-3543-6969 (2013) Julia and escaping set spiders' webs of positive area. International Mathematics Research Notices, 2015. 19-.

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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 B. This is also the first result on the area of a spider's web.

Item Type: Article
Uncontrolled Keywords: math.DS, math.DS, math.CV
Depositing User: Symplectic Admin
Date Deposited: 07 Apr 2017 08:34
Last Modified: 19 Jan 2023 07:06
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URI: https://livrepository.liverpool.ac.uk/id/eprint/3006833
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