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The dual nest for degenerate Yoccoz puzzles
Author(s):
Magnus
Aspenberg
Journal:
Conform. Geom. Dyn.
13
(2009),
187-196.
MSC (2000):
Primary 37F20;
Secondary 30D05
Posted:
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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Additional Information:
Magnus
Aspenberg
Affiliation:
Mathematisches Seminar, Christian-Albrechts Universität zu Kiel, Ludewig-Meyn Str.4, 24 098 Kiel, Germany
Email:
aspenberg@math.uni-kiel.de, maspenberg@gmail.com
DOI:
10.1090/S1088-4173-09-00197-0
PII:
S 1088-4173(09)00197-0
Received by editor(s):
April 8, 2009
Posted:
July 27, 2009
Additional Notes:
The author gratefully acknowledges funding from the Research Training Network CODY of the European Commission
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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