树映射有异状点的一个充要条件

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．

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

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.