华沙圈上连续自映射的周期点集的稳定性  

STABILITY OF PERIODIC ORBITS OF MAP ON WARSAW CIRCLE

作　　者：郭进峰[1] 

机构地区：[1]苏州城市建设环境保护学院基础部

出　　处：《松辽学刊（自然科学版）》1999年第1期33-35,共3页Songliao Journal (Natural Science Edition)

摘　　要：文［２］证明了华沙圈是一个Ｓａｒｋｏｖｓｋｉ空间．本文证明了其上任一连续自映射的周期点集是稳定的，也即对于任一华沙圈Ｗ上的连续满射ｆ：Ｗ→Ｗ，若ｆ有一ｎ—周期点，则存在ｆ的某一ε—邻域Ｕε（ｆ），使得对任意ｇ∈Ｕε（ｆ），和任意按Ｓａｒｋｏｖｓｋｉ序居于ｎ后面的正整数ｍ。Based on work, we know that W arsaw circle is a Sarkovskii space.In this paper the stability of periodic orbits of map on W arsaw circle is showed,that is,for any continuous map f from warsaw circle W onto itself if f has a periodic point of period n ,then there exists an ε-neighborhood u ε(f) in C( W,W ) such that for each g in u ε(f) and each positive integer m which lies to the behind n, according to the Sarkovskii's Order, g has a periodic point of period m .

关 键 词：华沙圈 周期点集 稳定性 S空间 连续自映射 

分 类 号：O175.12[理学—数学]