A combinatorial classification of postsingularly finite complex exponential maps

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September 2008, 22(3): 663-682. doi: 10.3934/dcds.2008.22.663

A combinatorial classification of postsingularly finite complex exponential maps

Bastian Laubner ^1, , Dierk Schleicher ^2, and Vlad Vicol ^3,

1.	Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
2.	School of Engineering and Science, Jacobs University Bremen, Postfach 750 561, D-28725 Bremen, Germany
3.	Department of Mathematics, University of Southern California, Los Angeles, CA 90089, United States

Received June 2007 Revised April 2008 Published August 2008

Abstract
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We give a combinatorial classification of postsingularly finite exponential maps in terms of external addresses starting with the entry $0$. This extends the classification results for critically preperiodic polynomials [2] to exponential maps. Our proof relies on the topological characterization of postsingularly finite exponential maps given recently in [14]. These results illustrate once again the fruitful interplay between combinatorics, topology and complex structure which has often been successful in complex dynamics.

Keywords: kneading sequence, postsingularly finite, external address, Exponential map, spider., classification.

Mathematics Subject Classification: Primary: 30D05, 37F10, 37F20; Secondary: 37F4.

Citation: Bastian Laubner, Dierk Schleicher, Vlad Vicol. A combinatorial classification of postsingularly finite complex exponential maps. Discrete & Continuous Dynamical Systems - A, 2008, 22 (3) : 663-682. doi: 10.3934/dcds.2008.22.663

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