广义sin(1/x)-连续统上连续自映射周期轨的稳定性

STABILITY OF PERIODIC ORBITS OF SELF-MAPS ON GENERALIZED sin1x-CONTINUUM

L.Block于1981年证明了区间映射的周期轨具有稳定性。即对于任一有界闭区间I上连续映射f:I→I,如果f有一n-周期轨,则存在f在C(I,I)中的一个邻域U,使得对于任意g∈U及任意在Sarkovskii序中居于n的右边的正整数m,g有m-周期轨。证明了广义sin1x-连续统上任一连续自映射的周期轨也具有稳定性。

The stability of periodic orbits of self-maps on a closed,bounded interval was proven by L.Block in 1981,it means that,for any continuous self-map f on a closed interval I with a periodic orbit of period n,there is a neighborhood U of f in C(I,I) such that for every g∈U and every position integer m with to the right of n in the Sarkovskii ordering,g has a periodic orbit of period m.In this paper,the stability of periodic orbits of self-maps on a generalized sin1x-continuum is obtained.