On the set where the iterates of an entire function are neither escaping nor bounded
Dynamical Systems
2016-10-03 v1 Complex Variables
Abstract
For a transcendental entire function f, we study the set of points BU(f) whose iterates under f neither escape to infinity nor are bounded. We give new results on the connectedness properties of this set and show that, if U is a Fatou component that meets BU(f), then most boundary points of U (in the sense of harmonic measure) lie in BU(f). We prove this using a new result concerning the set of limit points of the iterates of f on the boundary of a wandering domain. Finally, we give some examples to illustrate our results.
Keywords
Cite
@article{arxiv.1503.08077,
title = {On the set where the iterates of an entire function are neither escaping nor bounded},
author = {J. W. Osborne and D. J. Sixsmith},
journal= {arXiv preprint arXiv:1503.08077},
year = {2016}
}