Infinitely renormalizable quadratic polynomials

被引：12
|
作者：
Jiang, YP
机构：
[1] CUNY, Grad Ctr, Dept Math, New York, NY 10016 USA
[2] CUNY Queens Coll, Dept Math, Flushing, NY 11367 USA
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2000年 / 352卷 / 11期
关键词：
Julia set; local connectivity; two-dimensional puzzle; three-dimensional puzzle; infinitely renormalizable quadratic polynomial; complex bounds; unbranched;
D O I：
10.1090/S0002-9947-00-02514-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：5077 / 5091
页数：15
相关论文
共 50 条
  • [41] WICK POLYNOMIALS WITH A MASS GAP ARE NOT INFINITELY DIVISIBLE
    BAUMANN, K
    JOURNAL OF MATHEMATICAL PHYSICS, 1981, 22 (02) : 371 - 373
  • [42] On Functional Graphs of Quadratic Polynomials
    Mans, Bernard
    Sha, Min
    Shparlinski, Igor E.
    Sutantyo, Daniel
    EXPERIMENTAL MATHEMATICS, 2019, 28 (03) : 292 - 300
  • [43] QUADRATIC POLYNOMIALS AND HENON ATTRACTOR
    YOCCOZ, JC
    ASTERISQUE, 1991, (201) : 143 - 165
  • [44] IDEALS GENERATED BY QUADRATIC POLYNOMIALS
    Ananyan, Tigran
    Hochster, Melvin
    MATHEMATICAL RESEARCH LETTERS, 2012, 19 (01) : 233 - 244
  • [45] Mating Siegel quadratic polynomials
    Yampolsky, M
    Zakeri, S
    JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 14 (01) : 25 - 78
  • [46] SIBLING CURVES OF QUADRATIC POLYNOMIALS
    Wiggins, Harry
    Harding, Ansie
    Engelbrecht, Johann
    QUAESTIONES MATHEMATICAE, 2017, 40 (02) : 215 - 223
  • [47] Periodic orbits of quadratic polynomials
    Erkama, Timo
    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2006, 38 : 804 - 814
  • [48] Representations of integral quadratic polynomials
    Chan, Wai Kiu
    Oh, Byeong-Kweon
    DIOPHANTINE METHODS, LATTICES, AND ARITHMETIC THEORY OF QUADRATIC FORMS, 2013, 587 : 31 - +
  • [49] Quadratic polynomials at prime arguments
    Wu, Jie
    Xi, Ping
    MATHEMATISCHE ZEITSCHRIFT, 2017, 285 (1-2) : 631 - 646
  • [50] Multiplicative dependence of quadratic polynomials
    Dubickas A.
    Lithuanian Mathematical Journal, 1998, 38 (3) : 225 - 231
12345