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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 | References | Similar Articles | Additional Information


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

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

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