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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2024 MCQ for Conformal Geometry and Dynamics is 0.49.

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The dual nest for degenerate Yoccoz puzzles
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by Magnus Aspenberg
Conform. Geom. Dyn. 13 (2009), 187-196
DOI: https://doi.org/10.1090/S1088-4173-09-00197-0
Published electronically: July 27, 2009
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Abstract:

The Yoccoz puzzle is a fundamental tool in Holomorphic Dynamics. The original combinatorial argument by Yoccoz, based on the Branner-Hubbard tableau, counts the preimages of a non-degenerate annulus in the puzzle. However, in some important new applications of the puzzle (notably, matings of quadratic polynomials) there is no non-degenerate annulus. We develop a general combinatorial argument to handle this situation. It allows us to derive corollaries, such as the local connectedness of the Julia set, for suitable families of rational maps.
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Bibliographic Information
  • Magnus Aspenberg
  • Affiliation: Mathematisches Seminar, Christian-Albrechts Universität zu Kiel, Ludewig-Meyn Str.4, 24 098 Kiel, Germany
  • MR Author ID: 862979
  • Email: aspenberg@math.uni-kiel.de, maspenberg@gmail.com
  • Received by editor(s): April 8, 2009
  • Published electronically: July 27, 2009
  • Additional Notes: The author gratefully acknowledges funding from the Research Training Network CODY of the European Commission
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Conform. Geom. Dyn. 13 (2009), 187-196
  • MSC (2000): Primary 37F20; Secondary 30D05
  • DOI: https://doi.org/10.1090/S1088-4173-09-00197-0
  • MathSciNet review: 2525102