A NON SELF-SIMILAR SET

被引：0
|
作者：
D'Aniello, Emma [1 ]
Steele, T. H. [2 ]
机构：
[1] Seconda Univ Napoli, Scuola Politecn & Sci Base, Dipartimento Matemat & Fis, Viale Lincoln N5, I-81100 Caserta, Italy
[2] Weber State Univ, Dept Math, Ogden, UT 84408 USA
来源：
REAL ANALYSIS EXCHANGE | 2016年 / 41卷 / 02期
关键词：
iterated function system; attractor; self-similar set; Cantor set;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For each s epsilon (0, 1], we give an example of a nowhere dense perfect set E contained in the unit interval with dimH(E) = s, which is not an attractor for any iterated function system composed of weak contractions. This answers a problem posed by Zoltan Buczolich at the Summer Symposium in Real Analysis XXXIX (June 8-13, 2015, St. Olaf College, Northfield, MN).
引用
收藏
页码：347 / 350
页数：4
相关论文
共 50 条
  • [41] Self-similar and asymptotically self-similar solutions of nonlinear wave equations
    Hartmut Pecher
    Mathematische Annalen, 2000, 316 : 259 - 281
  • [42] FOURIER DECAY OF SELF-SIMILAR MEASURES AND SELF-SIMILAR SETS OF UNIQUENESS
    Varju, Peter P.
    Yu, Han
    ANALYSIS & PDE, 2022, 15 (03): : 843 - 858
  • [43] Rogue waves, self-similar statistics, and self-similar intermediate asymptotics
    Liang, Chunhao
    Ponomarenko, Sergey A.
    Wang, Fei
    Cai, Yangjian
    PHYSICAL REVIEW A, 2019, 100 (06)
  • [44] Self-similar and asymptotically self-similar solutions of nonlinear wave equations
    Pecher, H
    MATHEMATISCHE ANNALEN, 2000, 316 (02) : 259 - 281
  • [45] Self-similar pattern formation and continuous mechanics of self-similar systems
    Dyskin, A. V.
    HYDROLOGY AND EARTH SYSTEM SCIENCES, 2007, 11 (02) : 665 - 676
  • [46] Self-similar magnetoconductance fluctuations induced by self-similar periodic orbits
    Budiyono, A
    Nakamura, K
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2002, 71 (09) : 2090 - 2093
  • [47] Self-similar sets and self-similar measures in the p-adics
    Hare, Kevin George
    Vavra, Tomas
    JOURNAL OF FRACTAL GEOMETRY, 2024, 11 (3-4) : 247 - 287
  • [48] A CRITERION FOR A FINITE UNION OF INTERVALS TO BE A SELF-SIMILAR SET SATISFYING THE OPEN SET CONDITION*
    Wen, Zhi-Ying
    Zhao, Xuan
    ASIAN JOURNAL OF MATHEMATICS, 2017, 21 (01) : 185 - 195
  • [49] Algorithms to test open set condition for self-similar set related to PV numbers
    Li, Hao
    Guo, Qiu-Li
    Wang, Qin
    Xi, Li-Feng
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 421 (01) : 453 - 473
  • [50] Self-similar collapse with non-radial motions
    Nusser, A.
    MASS PROFILES AND SHAPES OF COSMOLOGICAL STRUCTURES, 2006, 20 : 1 - 4
12345