The Hausdorff measure of the self-similar sets——The Koch curve

被引：0
|
作者：
周作领
机构：
来源：
Science in China,SerA. | 1998年 / Ser.A.1998卷 / 07期
关键词：
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The self similar sets satisfying the open condition have been studied. An estimation of fractal, by the definition can only give the upper limit of its Hausdorff measure. So to judge if such an upper limit is its exact value or not is important. A negative criterion has been given. As a consequence, the Marion's conjecture on the Hausdorff meas\| ure of the Koch curve has been proved invalid.
引用
收藏
页码：723 / 728
页数：6
相关论文
共 50 条
  • [41] Lacunarity of self-similar and stochastically self-similar sets
    Gatzouras, D
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (05) : 1953 - 1983
  • [42] Positive-measure self-similar sets without interior
    Csornyei, M.
    Jordan, T.
    Pollicott, M.
    Preiss, D.
    Solomyak, B.
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2006, 26 : 755 - 758
  • [43] Computability of the packing measure of totally disconnected self-similar sets
    Llorente, Marta
    Moran, Manuel
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2016, 36 : 1534 - 1556
  • [44] On the computing of the appoximate value of the Hausdorff measure of Koch curve
    Xu, S.
    Zeng, S.
    [J]. Gongcheng Shuxue Xuebao/Chinese Journal of Engineering Mathematics, 2001, 18 (01): : 83 - 88
  • [45] Finite type in measure sense for self-similar sets with overlaps
    Deng, Juan
    Wen, Zhiying
    Xi, Lifeng
    [J]. MATHEMATISCHE ZEITSCHRIFT, 2021, 298 (1-2) : 821 - 837
  • [46] Finite type in measure sense for self-similar sets with overlaps
    Juan Deng
    Zhiying Wen
    Lifeng Xi
    [J]. Mathematische Zeitschrift, 2021, 298 : 821 - 837
  • [47] A REMARK ON SELF-SIMILAR SUBSETS OF UNIFORM CANTOR SETS WITH SMALL HAUSDORFF DIMENSION
    Rao, Hui
    Wen, Zie-Ying
    Zeng, Ying
    [J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2020, 28 (04)
  • [48] From Self-Similar Groups to Self-Similar Sets and Spectra
    Grigorchuk, Rostislav
    Nekrashevych, Volodymyr
    Sunic, Zoran
    [J]. FRACTAL GEOMETRY AND STOCHASTICS V, 2015, 70 : 175 - 207
  • [49] JULIA SETS AND SELF-SIMILAR SETS
    KAMEYAMA, A
    [J]. TOPOLOGY AND ITS APPLICATIONS, 1993, 54 (1-3) : 241 - 251
  • [50] On the distance sets of self-similar sets
    Orponen, Tuomas
    [J]. NONLINEARITY, 2012, 25 (06) : 1919 - 1929
12345