English

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 UU for which the singular value is accessible both from the set of escaping points and from UU 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