Continuous dependence on parameters of self-affine sets and measures

被引:0
作者
Deng, Qirong [1 ]
Li, Mingtian [1 ]
Yao, Yonghua [1 ]
机构
[1] Fujian Normal Univ, Sch Math & Stat, Fuzhou 350117, Fujian, Peoples R China
关键词
Self-affine set; Self-affine measure; Convergence; ITERATED FUNCTION SYSTEMS;
D O I
10.1016/j.chaos.2022.112309
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
For the sequences of self-affine measures mu A(n),D-n,P-n and self-affine sets T (A(n), D-n ), the relation between their convergence and the convergence of the sequence (A(n), D-n, P-n)(n=1)(infinity) are considered. Several interesting results are obtained.(C) 2022 Elsevier Ltd. All rights reserved.
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页数:7
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共 12 条
  • [1] On the inverse fractal problem for two-dimensional attractors
    Deliu, A
    Geronimo, J
    Shonkwiler, R
    [J]. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1997, 355 (1726): : 1017 - 1062
  • [2] Uniformity of spectral self-affine measures
    Deng, Qi-Rong
    Chen, Jian-Bao
    [J]. ADVANCES IN MATHEMATICS, 2021, 380
  • [3] The intersections of self-similar and self-affine sets with their perturbations under the weak separation condition
    Deng, Qi-Rong
    Wang, Xiang-Yang
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2018, 38 : 1353 - 1368
  • [4] Deng QR, 2017, J FRACTAL GEOM, V4, P43, DOI 10.4171/JFG/44
  • [5] On the equivalence of homogeneous iterated function systems
    Deng, Qi-Rong
    Lau, Ka-Sing
    [J]. NONLINEARITY, 2013, 26 (10) : 2767 - 2775
  • [6] CONTINUOUS DEPENDENCE ON PARAMETERS OF CERTAIN SELF-AFFINE MEASURES, AND THEIR SINGULARITY
    Ding, Daoxin
    [J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 2011, 61 (02) : 495 - 508
  • [7] On the structures of generating iterated function systems of Cantor sets
    Feng, De-Jun
    Wang, Yang
    [J]. ADVANCES IN MATHEMATICS, 2009, 222 (06) : 1964 - 1981
  • [8] Open set condition and pseudo Hausdorff measure of self-affine IFSs
    Fu, Xiaoye
    Gabardo, Jean-Pierre
    Qiu, Hua
    [J]. NONLINEARITY, 2020, 33 (06) : 2592 - 2614
  • [9] On a generalized dimension of self-affine fractals
    He, Xing-Gang
    Lau, Ka-Sing
    [J]. MATHEMATISCHE NACHRICHTEN, 2008, 281 (08) : 1142 - 1158
  • [10] FRACTALS AND SELF SIMILARITY
    HUTCHINSON, JE
    [J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1981, 30 (05) : 713 - 747