Self-similar measures on the Julia sets of polynomials

被引：0
|
作者：
周吉
邱维元
任福尧
机构：
[1] China
[2] Department of Mathematics
[3] Fudan University
[4] Shanghai 200433
来源：
Progress in Natural Science | 2000年 / 04期
基金：
中国国家自然科学基金;
关键词：
invariant measure; self-similar measure; Fatou set; Julia set; critical point;
D O I：
暂无
中图分类号：
O174.14 [多项式理论];
学科分类号：
摘要：
If the immediate basin of infinity of a polynomial P(z) contains at least one of its critical points, then there is a self-similar measure on its Julia set, and if all the critical points of P(z) lie in the immediate basin of infinity, then the self-similar measure is unique.
引用
收藏
页码：28 / 33
页数：6
相关论文
共 50 条
  • [31] Topological measures, image transformations and self-similar sets
    Aarnes, JF
    Johansen, O
    Rustad, AB
    ACTA MATHEMATICA HUNGARICA, 2005, 109 (1-2) : 65 - 97
  • [32] Curvature-direction measures of self-similar sets
    Bohl, Tilman Johannes
    Zaehle, Martina
    GEOMETRIAE DEDICATA, 2013, 167 (01) : 215 - 231
  • [33] Lacunarity of self-similar and stochastically self-similar sets
    Gatzouras, D
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (05) : 1953 - 1983
  • [34] Normal and non-normal points of self-similar sets and divergence points of self-similar measures
    Olsen, L
    Winter, S
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2003, 67 : 103 - 122
  • [35] THE CENTERED COVERING MEASURES OF A CLASS OF SELF-SIMILAR SETS ON THE PLANE
    Zhu, Zhiwei
    Zhou, Zuoling
    REAL ANALYSIS EXCHANGE, 2007, 33 (01) : 215 - 231
  • [36] An algorithm for computing the centered Hausdorff measures of self-similar sets
    Llorente, Marta
    Moran, Manuel
    CHAOS SOLITONS & FRACTALS, 2012, 45 (03) : 246 - 255
  • [37] Exact dimensionality and projections of random self-similar measures and sets
    Falconer, Kenneth J.
    Jin, Xiong
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2014, 90 : 388 - 412
  • [38] Density theorems for Hausdorff and packing measures of self-similar sets
    Lars Olsen
    Aequationes mathematicae, 2008, 75 : 208 - 225
  • [39] Density theorems for Hausdorff and packing measures of self-similar sets
    Olsen, Lars
    AEQUATIONES MATHEMATICAE, 2008, 75 (03) : 208 - 225
  • [40] From Self-Similar Groups to Self-Similar Sets and Spectra
    Grigorchuk, Rostislav
    Nekrashevych, Volodymyr
    Sunic, Zoran
    FRACTAL GEOMETRY AND STOCHASTICS V, 2015, 70 : 175 - 207
12345