Sensitivity and regionally proximal relation in minimal systems  

作　　者：SHAO Song YE XiangDong ZHANG RuiFeng 

机构地区：[1]Department of Mathematics,University of Science and Technology of China,Hefei 230026,China

出　　处：《Science China Mathematics》2008年第6期987-994,共8页中国科学：数学（英文版）

基　　金：the National Natural Science Foundation of China(Grant Nos.10501042,10531010);the Ministry of Education of China(Grant No.20050358053)

摘　　要：A topological dynamical system is n-sensitive,if there is a positive constant such that in each non-empty open subset there are n distinct points whose iterates will be apart from the constant at least for a same moment.The properties of n-sensitivity in minimal systems are investigated.It turns out that a minimal system is n-sensitive if and only if the n-th regionally proximal relation Q_n contains a point whose coordinates are pairwise distinct.Moreover,the structure of a minimal system which is n-sensitive but not(n+1)-sensitive(n≥2)is determined.A topological dynamical system is n-sensitive, if there is a positive constant such that in each non-empty open subset there are n distinct points whose iterates will be apart from the constant at least for a same moment. The properties of n-sensitivity in minimal systems are investigated. It turns out that a minimal system is n-sensitive if and only if the n-th regionally proximal relation Q n contains a point whose coordinates are pairwise distinct. Moreover, the structure of a minimal system which is n-sensitive but not (n + 1)-sensitive (n ? 2) is determined.

关 键 词：sensitivity n-sensitivity regionally proximal relation MINIMALITY 37B05 

分 类 号：O19[理学—数学] O189[理学—基础数学]