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2008, Volume 22, Issue 3: 663-682. Doi: 10.3934/dcds.2008.22.663
This issue Previous Article The complete classification on a model of two species competition with an inhibitor Next Article Resonant decompositions and the $I$-method for the cubic nonlinear Schrödinger equation on $\mathbb{R}^2$

A combinatorial classification of postsingularly finite complex exponential maps

  • 1.

    Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin

  • 2.

    School of Engineering and Science, Jacobs University Bremen, Postfach 750 561, D-28725 Bremen

  • 3.

    Department of Mathematics, University of Southern California, Los Angeles, CA 90089

Received:  June 2007
Revised:  April 2008
Published:  September 2008
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: Primary: 30D05, 37F10, 37F20; Secondary: 37F45.

    Citation:
    shu

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