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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Infinitely Renormalizable Quadratic Polynomials
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by Yunping Jiang
Trans. Amer. Math. Soc. 352 (2000), 5077-5091
DOI: https://doi.org/10.1090/S0002-9947-00-02514-9
Published electronically: July 12, 2000

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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Bibliographic 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
  • MR Author ID: 238389
  • Email: yunqc@jiang.math.qc.edu
  • 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
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 5077-5091
  • MSC (2000): Primary 37Fxx; Secondary 37E20
  • DOI: https://doi.org/10.1090/S0002-9947-00-02514-9
  • MathSciNet review: 1675198