SCRAMBLED CANTOR SETS

被引：1
|
作者：
Geschke, Stefan [1 ]
Grebik, Jan [2 ]
Miller, Benjamin D. [3 ]
机构：
[1] Univ Hamburg, Dept Math, Bundesstr 55, D-20146 Hamburg, Germany
[2] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England
[3] Univ Wien, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 149卷 / 10期
关键词：
Asymptotic; chaos; Li-Yorke; proximal;
D O I：
10.1090/proc/15532
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that Li-Yorke chaos ensures the existence of a scrambled Cantor set.
引用
收藏
页码：4461 / 4468
页数：8
相关论文
共 50 条
  • [1] Cardinalities of scrambled sets and positive scrambled sets
    Mai, Jiehua
    Zhou, Lei
    Sun, Taixiang
    TOPOLOGY AND ITS APPLICATIONS, 2024, 342
  • [2] ON INVARIANT ε-SCRAMBLED SETS
    Balibrea, Francisco
    Guirao, Juan L. G.
    Oprocha, Piotr
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2010, 20 (09): : 2925 - 2935
  • [3] Dense invariant open distributionally scrambled sets and closed distributionally scrambled sets
    Wang, Hui
    Lei, Fengchun
    Wang, Lidong
    TOPOLOGY AND ITS APPLICATIONS, 2014, 165 : 110 - 120
  • [4] Rank 2 proximal Cantor systems are residually scrambled
    Shimomura, Takashi
    DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2018, 33 (02): : 275 - 302
  • [5] On scrambled sets and a theorem of Kuratowski on independent sets
    Kato, H
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (07) : 2151 - 2157
  • [6] Scrambled sets of shift operators
    Wu, Xinxing
    Chen, Guanrong
    JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9 (05): : 2631 - 2637
  • [7] On n-scrambled sets
    Yang, Qigui
    Yang, Xiaofang
    TOPOLOGY AND ITS APPLICATIONS, 2024, 344
  • [8] SYNDETIC PROXIMALITY AND SCRAMBLED SETS
    Moothathu, T. K. Subrahmonian
    Oprocha, Piotr
    TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2013, 41 (02) : 421 - 461
  • [9] ON SCRAMBLED SETS FOR CHAOTIC FUNCTIONS
    BRUCKNER, AM
    HU, TY
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 301 (01) : 289 - 297
  • [10] A Remark on Invariant Scrambled Sets
    Huang, Lin
    Wang, Huoyun
    Wu, Hongying
    PROGRESS IN INDUSTRIAL AND CIVIL ENGINEERING, PTS. 1-5, 2012, 204-208 : 4776 - +
12345