Distributionally scrambled set and minimal set

作     者：WANG LiDong WANG Hui 

作者机构：Department of MathematicsDalian Nationalities University School of Mathematical SciencesDalian University of Technology 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2014年第57卷第9期

页      面：1953-1960页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the Independent Research Foundation of the Central Universities(Grant No.DC 12010111) National Natural Science Foundation of China(Grant No.11271061) 

主　　题：distributional chaos minimal set 

摘      要：We investigate the relation between distributional chaos and minimal sets,and discuss how to obtain various distributionally scrambled sets by using least and simplest minimal *** show:i)an uncountable extremal distributionally scrambled set can appear in a system with just one simple minimal set:a periodic orbit with period 2;ii)an uncountable dense invariant distributionally scrambled set can occur in a system with just two minimal sets:a fixed point and an infinite minimal set;iii)infinitely many minimal sets are necessary to generate a uniform invariant distributionally scrambled set,and an uncountable dense extremal invariant distributionally scrambled set can be constructed by using just countably infinitely many periodic orbits.