树映射有异状点的一个充要条件  

A Necessary and Sufficient Condition for Continuous Maps of a Tree to Have a Homoclinic point

作　　者：牛应轩[1] 

机构地区：[1]安徽省六安师范专科学校数学系

出　　处：《数学研究》1999年第3期272-276,共5页Journal of Mathematical Study

摘　　要：讨论了树上连续自映射的拓扑熵与非稳定流形之间的关系． 证明了：树上连续自映射有异状点的充要条件是其拓扑熵大于零． 因而推广了区间上连续自映射的一个结果．Let f be a continuous map of a tree into itself. In this paper, we discuss the relations between the topological entropy and unstable mainifolds. It is shown that f has a homoclinic point if and only if its topological entropy is positive. Obviously, this result is a generalization of that of a continuous itself map of the interval.

关 键 词：树 异状点 拓扑熵 非稳定流形 连续自映射 动力系统 拓扑空间 

分 类 号：O189.3[理学—数学]