度量空间上自映射有异状点的一个充要条件

A Necessary and Sufficient Condition of Homoclinic Points for a Self-mapping on the Metric Space

设f是N维度量空间到自身的可降自映射,给出了f有异状点的一个充要条件为存在链回归点但不是周期点,且f的ω-极限集与周期点集的交非空.

If f is a reduced self-mapping of the N-dimensional metric space to itself, Here this paper pres-ents a necessary and sufficient condition for f with homochinic points：Existences chain recurrent but not peri-odic point, and the ω-limiting point set and periodic point set is nonempty intersection.