On Nonlanding Dynamic Rays of Exponential Maps

Abstract

We consider the case of an exponential map Eκ : z 7→ exp(z) + κ for which the singular value κ is accessible from the set of escaping points of Eκ. We show that there are dynamic rays of Eκ 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 U for which the singular value is accessible both from the set of escaping points and from U contains uncountably many indecomposable continua.

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Cite this paper

@inproceedings{Rempe2005OnND, title={On Nonlanding Dynamic Rays of Exponential Maps}, author={Lasse Rempe}, year={2005} }