A note on distributional chaos with respect to a sequence

被引：8
作者：
Oprocha, Piotr [1 ]
机构：
[1] AGH Univ Sci & Technol, Fac Appl Math, PL-30059 Krakow, Poland
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 11期
关键词：
Distributional chaos; Weak mixing; Topological entropy;
D O I：
10.1016/j.na.2009.04.066
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The aim of this note is to use methods developed by Kuratowski and Mycielski to prove that some more common notions in topological dynamics imply distributional chaos with respect to a sequence. In particular, we show that the notion of distributional chaos with respect to a sequence is only slightly stronger than the definition of chaos due to Li and Yorke. Namely, positive topological entropy and weak mixing both imply distributional chaos with respect to a sequence, which is not the case for distributional chaos as introduced by Schweizer and Smital. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码：5835 / 5839
页数：5
相关论文
共 18 条
[1]  
Akin E., 2004, CONT MATH, V356, P21
[2]   The three versions of distributional chaos [J].
Balibrea, F ;
Smítal, J ;
Stefánková, M .
CHAOS SOLITONS & FRACTALS, 2005, 23 (05) :1581-1583
[3]  
Blanchard F, 2002, J REINE ANGEW MATH, V547, P51
[4]  
Blanchard F., 2008, C MATH, V110, P293, DOI DOI 10.4064/CM110-2-3.MR2353910
[5]  
DERKER M, 1976, ERGODIC THEORY COMPA
[6]  
Furstenberg H., 1967, Math. Syst. Theory, V1, P1, DOI [10.1007/BF01692494, DOI 10.1007/BF01692494]
[7]   Devaney's chaos or 2-scattering implies Li-Yorke's chaos [J].
Huang, W ;
Ye, XD .
TOPOLOGY AND ITS APPLICATIONS, 2002, 117 (03) :259-272
[8]  
Illanes A., 1999, Monographs and Textbooks in Pure and Applied Mathematics, V216
[9]  
Iwanik A., 1991, Independence and Scrambled Sets for Chaotic Mappings. The mathematical heritage of C. F. Gauss, P372, DOI DOI 10.1142/97898145034570027
[10]   On scrambled sets and a theorem of Kuratowski on independent sets [J].
Kato, H .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (07) :2151-2157
12