Distributionally scrambled set and minimal set  

作　　者：WANG LiDong WANG Hui 

机构地区：[1]Department of Mathematics,Dalian Nationalities University [2]School of Mathematical Sciences,Dalian University of Technology

出　　处：《Science China Mathematics》2014年第9期1953-1960,共8页中国科学：数学（英文版）

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)

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 sets.We 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.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 sets.We 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.

关 键 词：distributional chaos minimal set 

分 类 号：O144[理学—数学]