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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The role of the Ahlfors five islands theorem in complex dynamics
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by Walter Bergweiler PDF
Conform. Geom. Dyn. 4 (2000), 22-34 Request permission

Abstract:

The Ahlfors five islands theorem has become an important tool in complex dynamics. We discuss its role there, describing how it can be used to deal with a variety of problems. This includes questions concerning the Hausdorff dimension of Julia sets, the existence of singleton components of Julia sets, and the existence of repelling periodic points. We point out that for many applications a simplified version of the Ahlfors five islands theorem suffices, and we give an elementary proof of this version.
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Additional Information
  • Walter Bergweiler
  • Affiliation: Mathematisches Seminar, Christian–Albrechts–Universität zu Kiel, Ludewig–Meyn–Str. 4, D–24098 Kiel, Germany
  • MR Author ID: 35350
  • Email: bergweiler@math.uni-kiel.de
  • Received by editor(s): October 29, 1999
  • Published electronically: March 14, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 4 (2000), 22-34
  • MSC (2000): Primary 30C25; Secondary 30D05, 30D45, 37F10
  • DOI: https://doi.org/10.1090/S1088-4173-00-00057-6
  • MathSciNet review: 1741773