We introduce the notion of measurable n-sensitivity for measure preserving systems,and study the relation between measurable n-sensitivity and the maximal pattern entropy.We prove that,if(X,ℬ,μ,T)is ergodic,then(X,ℬ,...We introduce the notion of measurable n-sensitivity for measure preserving systems,and study the relation between measurable n-sensitivity and the maximal pattern entropy.We prove that,if(X,ℬ,μ,T)is ergodic,then(X,ℬ,μ,T)is measurable n-sensitive but not measurable(n+1)-sensitive if and only if h_(μ)^(*)(T)=log n,where h_(μ)^(*)(T)is the maximal pattern entropy of T.展开更多
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 mome...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.展开更多
基金supported in part by the National Natural Science Foundation of China(Grant Nos.11871188,12031019).
文摘We introduce the notion of measurable n-sensitivity for measure preserving systems,and study the relation between measurable n-sensitivity and the maximal pattern entropy.We prove that,if(X,ℬ,μ,T)is ergodic,then(X,ℬ,μ,T)is measurable n-sensitive but not measurable(n+1)-sensitive if and only if h_(μ)^(*)(T)=log n,where h_(μ)^(*)(T)is the maximal pattern entropy of T.
基金the National Natural Science Foundation of China(Grant Nos.10501042,10531010)the Ministry of Education of China(Grant No.20050358053)
文摘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.
