一类正方形连续自映射有素周期点的一个必要条件

Necessary Condition of Continuous Self-mapping of a Class of the Square with Prime Periodic Points

设f为单位正方形到自身的连续映射,(?)是f的下降,本文给出了这类正方形连续自映射有素周期点的一个必要条件——存在x∈Ω(f)x是准周期点但不是周期点。

Let f be a continuous map of a unit square into itself, f is a descent of f. In this paper, the writer mainly gives proof of a condition which is necessary for self-mapping of this class to have prime periodic points. Namely, f has prime periodic points only if there is a point xeO(f), that is, x is not a periodic point but an eventually periodic point.