强初值敏感性的一些性质及充分条件  

Some Properties and Sufficient Conditions on the Strong Sensitivity to Initial Conditions

作　　者：牛应轩[1] 汪轶[1] 

机构地区：[1]皖西学院数理系,安徽六安237012

出　　处：《皖西学院学报》2010年第2期1-3,6,共4页Journal of West Anhui University

基　　金：安徽省教育厅自然科学研究项目(KJ2007B123);皖西学院自然科学青年项目(WXQZ0602)

摘　　要：设X为紧致度量空间,f:X→X为连续映射,讨论了强初值敏感性的一些性质,证明了(X,f)是强初值敏感的当且仅当其自然扩充是强初值敏感的,并给出系统(X,f)是强初值敏感的充分条件,另外证明了如果(X,f)是拓扑混合的或是区间上拓扑传递的,那么(X,f)是强初值敏感的。Let X be a compact metric space and f：X→X continuous.In this paper,some properties of the strongly sensitive dependence on initial conditions are discussed,it is obtained that（X,f） is strongly sensitive if and only if so is its natural extension,and some sufficient conditions for（X,f）to be strongly sensitive are obtained.What＇s more,it is shown that if（X,f） is topological mixing or topologically transitive on the interval,then（X,f） is strongly sensitive.

关 键 词：强初值敏感性 初值敏感性 拓扑混合 拓扑传递 

分 类 号：O189.11[理学—数学]