湍流、不动点与周期轨的稳定性

Turbulent、the Fixed Point and the Stability of the Periodic Orbit

本文对区间连续自映射,讨论了湍流与不动点的关系:若x0∈I及ω(x0,f)中的不动点c,满足:c<x0<f(x0)或f(x0)<x0<c,则f是湍流;证明了简单奇周期轨具有稳定性,并得到若f的所有周期轨都是简单周期轨,则ε>0,对g∈ωε(f),g的所有周期轨也都是简单的。

In this paper,the relation about turbulent and the fixed point is discussed briefly：Let f：I→I be a continuous map,if x0∈I,c∈ω（x0,f） and f（c）=c such that： cx0f（x0） or f（x0）x0c,then f is turbulent;the stability of simple odd periodic orbit is proved,and if all of periodic orbit of f is simple,then ε0,g∈ωε（f）,all of periodic orbit of g is simple..