Minimality and distributional chaos in triangular maps

被引:0
作者
Balibrea, Francisco [1 ]
Rucka, Lenka [2 ]
机构
[1] Univ Murcia, Dept Math, Murcia 30100, Spain
[2] Silesian Univ Opava, Math Inst, Opava, Czech Republic
关键词
Minimality; triangular maps; distributional chaos; Sharkovsky classification; 3; VERSIONS;
D O I
10.1080/10236198.2023.2293114
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The result of this paper contributes to the classification of triangular maps of the square with zero topological entropy stated by A. N. Sharkovsky in the 1980s. The problem was if a triangular map of the square such that its any omega-limit set contains unique minimal set can be distributionally chaotic. So far such result was disproved only for the class of triangular maps non-decreasing on fibres [L. Paganoni, J. Smital, Strange distributionally chaotic triangular maps, Chaos Solitons Fractals 26(2) (2005), pp. 581-589]. In this paper, we solve the problem in negative for all triangular maps of the square, correcting the original result from Balibrea and Smital [Strong distributional chaos and minimal sets, Topology appl. 156 (2009), pp. 1673-1678].
引用
收藏
页码:1662 / 1670
页数:9
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