## Institute for Mathematical Sciences

## Preprint ims99-9

** D. Schleicher and J. Zimmer**
* Dynamic Rays for Exponential Maps*

Abstract: We discuss the dynamics of exponential maps $z\mapsto \lambda e^z$ from the point of view of dynamic
rays, which have been an important tool for the study of
polynomial maps. We prove existence of dynamic rays with
bounded combinatorics and show that they contain all points
which ``escape to infinity'' in a certain way. We then discuss
landing properties of dynamic rays and show that in many
important cases, repelling and parabolic periodic points are
landing points of periodic dynamic rays. For the case of
postsingularly finite exponential maps, this needs the use of
spider theory.

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