连续映射的弱specification性质与混沌  

Continuous map considering the weak specification property and chaos

作　　者：乔宗敏[1] 朱夜明[2] 顾荣宝[3] 

机构地区：[1]安徽大学计算智能与信号处理教育部重点实验室,安徽合肥230039 [2]安徽大学学报编辑部,安徽合肥230039 [3]南京财经大学数学系,江苏南京210003

出　　处：《合肥工业大学学报（自然科学版）》2004年第9期1066-1069,共4页Journal of Hefei University of Technology：Natural Science

基　　金：安徽省高等学校青年教师科研资助项目(2003j154)

摘　　要：specification性质是一种重要的动力性质,对连续的区间映射和树映射,该性质与拓扑混合等价。对紧致度量空间,满足POTP性质的拓扑混合映射具有specification性质。文章对紧致度量空间上连续自映射,研究了弱specification性质与各种混沌之间的关系,证明了具有弱specification性质的系统是Li-Yorke意义下混沌的,是Ruelle-Takens意义下混沌的,是处处混沌的,并且具有性质P。Specification is an important dynamical property, and it is equivalent to topological mixing for continuous mapping on the interval and the tree,and for the continuous map of compact metric space,POTP and topological mixing imply weak specification. Here studied are the relationships between the weak specification property and all kinds of chaos. It is proved that the system with weak specification must be Li-Yorke chaos, Ruelle-Takens chaos,chaos everywhere,and having the property of P.

关 键 词：连续自映射 弱specification 混沌 

分 类 号：O192[理学—数学]