A combinatorial classification of postsingularly finite complex exponential maps

Bastian Laubner, Dierk Schleicher, Vlad Vicol

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)663-682
Number of pages20
JournalDiscrete and Continuous Dynamical Systems
Volume22
Issue number3
StatePublished - Nov 1 2008

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Exponential Map
Complex Dynamics
Combinatorics
Complex Structure
Topology
Polynomials
Polynomial

Keywords

  • Classification
  • Exponential map
  • External address
  • Kneading sequence
  • Postsingularly finite
  • Spider

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

A combinatorial classification of postsingularly finite complex exponential maps. / Laubner, Bastian; Schleicher, Dierk; Vicol, Vlad.

In: Discrete and Continuous Dynamical Systems, Vol. 22, No. 3, 01.11.2008, p. 663-682.

Research output: Contribution to journalArticle

Laubner, Bastian ; Schleicher, Dierk ; Vicol, Vlad. / A combinatorial classification of postsingularly finite complex exponential maps. In: Discrete and Continuous Dynamical Systems. 2008 ; Vol. 22, No. 3. pp. 663-682.
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