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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Infinitely Renormalizable Quadratic Polynomials


Author: Yunping Jiang
Journal: Trans. Amer. Math. Soc. 352 (2000), 5077-5091
MSC (2000): Primary 37Fxx; Secondary 37E20
Published electronically: July 12, 2000
MathSciNet review: 1675198
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Abstract:

We prove that the Julia set of a quadratic polynomial which admits an infinite sequence of unbranched, simple renormalizations with complex bounds is locally connected. The method in this study is three-dimensional puzzles.


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Additional Information

Yunping Jiang
Affiliation: Department of Mathematics, CUNY Graduate Center, 365 Fifth Avenue, New York, New York 10016 and Department of Mathematics, Queens College of CUNY, Flushing, New York 11367
Email: yunqc@jiang.math.qc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02514-9
PII: S 0002-9947(00)02514-9
Keywords: Julia set, local connectivity, two-dimensional puzzle, three-dimensional puzzle, infinitely renormalizable quadratic polynomial, complex bounds, unbranched
Received by editor(s): September 25, 1997
Received by editor(s) in revised form: January 14, 1999
Published electronically: July 12, 2000
Additional Notes: The author is supported in part by grants from the NSF and from the PSC-CUNY
Article copyright: © Copyright 2000 American Mathematical Society