Dimensions of slowly escaping sets and annular itineraries for exponential functions

Sixsmith, Dave (2016). Dimensions of slowly escaping sets and annular itineraries for exponential functions. Ergodic Theory and Dynamical Systems, 36(7) pp. 2273–2292.

DOI: https://doi.org/10.1017/etds.2015.7

Abstract

We study the iteration of functions in the exponential family. We construct a number of sets, consisting of points which escape to infinity ‘slowly’, and which have Hausdorff dimension equal to 1. We prove these results by using the idea of an annular itinerary. In the case of a general transcendental entire function we show that one of these sets, the uniformly slowly escaping set, has strong dynamical properties and we give a necessary and sufficient condition for this set to be non-empty.

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About

• Item ORO ID
• 41763
• Item Type
• Journal Item
• ISSN
• 1469-4417
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Dimensions in complex dynamics: spiders' webs and speed of escape. (XM-11-079-GS)	EP/J022160/1	EPSRC

• Extra Information
• 20 pp.
• 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 Cambridge University Press,
• Depositing User
• Dave Sixsmith