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A Combinatorial Classification of Postsingularly Finite Complex Exponential Maps

Bastian Laubner·Dierk Schleicher·Vlad Vicol
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Abstract

We give a combinatorial classification of postsingularly finite exponential maps in terms of external addresses starting with the entry 0. This is an extension of the classification results for critically preperiodic polynomials \cite{BFH} to exponential maps. Our proof relies on the topological characterization of postsingularly finite exponential maps given recently in \cite{HSS}. Our results illustrate once again the fruitful interplay between combinatorics, topology and complex structure which has often been successful in complex dynamics.

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Bastian Laubner, Dierk Schleicher, Vlad Vicol. 2006-02-27. A Combinatorial Classification of Postsingularly Finite Complex Exponential Maps. https://arxiv.org/abs/math/0602602

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