Dimensions of slowly escaping sets and annular itineraries for exponential functions
Dynamical Systems
2019-02-20 v1 Complex Variables
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.
Keywords
Cite
@article{arxiv.1407.4638,
title = {Dimensions of slowly escaping sets and annular itineraries for exponential functions},
author = {D. J. Sixsmith},
journal= {arXiv preprint arXiv:1407.4638},
year = {2019}
}