Classification of escaping exponential maps

Förster, Markus; Rempe, Lasse; Schleicher, Dierk

doi:10.1090/S0002-9939-07-09073-9

Classification of escaping exponential maps
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by Markus Förster, Lasse Rempe and Dierk Schleicher

Proc. Amer. Math. Soc. 136 (2008), 651-663

DOI: https://doi.org/10.1090/S0002-9939-07-09073-9

Published electronically: November 1, 2007

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Abstract:

We give a complete classification of the set of parameters $\kappa$ for which the singular value of $E_{\kappa }:z\mapsto \exp (z)+\kappa$ escapes to $\infty$ under iteration. In particular, we show that every path-connected component of this set is a curve to infinity.

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