Dynamic rays of bounded-type entire functions
Dynamical Systems
2011-01-07 v2 Complex Variables
General Topology
Abstract
We construct an entire function in the Eremenko-Lyubich class whose Julia set has only bounded path-components. This answers a question of Eremenko from 1989 in the negative. On the other hand, we show that for many functions in , in particular those of finite order, every escaping point can be connected to by a curve of escaping points. This gives a partial positive answer to the aforementioned question of Eremenko, and answers a question of Fatou from 1926.
Keywords
Cite
@article{arxiv.0704.3213,
title = {Dynamic rays of bounded-type entire functions},
author = {Günter Rottenfußer and Johannes Rückert and Lasse Rempe and Dierk Schleicher},
journal= {arXiv preprint arXiv:0704.3213},
year = {2011}
}