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Infinitely Renormalizable Quadratic Polynomials
Author(s):
Yunping
Jiang
Journal:
Trans. Amer. Math. Soc.
352
(2000),
5077-5091.
MSC (2000):
Primary 37Fxx;
Secondary 37E20
Posted:
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:
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
Posted:
July 12, 2000
Additional Notes:
The author is supported in part by grants from the NSF and from the PSC-CUNY
Copyright of article:
Copyright
2000,
American Mathematical Society
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