On Nonlanding Dynamic Rays of Exponential Maps
Dynamical Systems
2007-10-28 v2 Complex Variables
Abstract
We consider the case of an exponential map for which the singular value is accessible from the set of escaping points. We show that there are dynamic rays of which do not land. In particular, there is no analog of Douady's ``pinched disk model'' for exponential maps whose singular value belongs to the Julia set. We also prove that the boundary of a Siegel disk for which the singular value is accessible both from the set of escaping points and from contains uncountably many indecomposable continua.
Keywords
Cite
@article{arxiv.math/0511588,
title = {On Nonlanding Dynamic Rays of Exponential Maps},
author = {Lasse Rempe},
journal= {arXiv preprint arXiv:math/0511588},
year = {2007}
}
Comments
15 pages; 1 figure. V2: A result on Siegel disks, as well as a figure, has been added. Some minor corrections were also made