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Sixsmith, Dave
(2015).
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
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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