N维单位体上连续映射有素周期点的条件

Condition of the continuous self-mapping of unit solid body in R^n with prime periodic points

对于一类N维单位体到自身的连续映射f,我们利用了f的下降F以及Sharkovskii定理给出了这种映射有素周期点的一个必要条件———设F是f的下降,如果f有素周期点,则存在x∈Ω(f),使x是准周期点,但不是周期点。

Letf be a continuous map of aunit solid body in Rn. F is adescent off. Using the descert property off and Sharrkovkii thorem, a necessary condition for this class of self-mapping existing a prime periodic point is given,namely ,if F is adescent off,f has prime periodic points,there is a point x∈Ω（f） then x is not a periodic point,but an eventully periodic point.