单峰映射的周期轨序

Period orbit series in unimodal maps

连续单峰映射f在f(xmin)≤xt,f(xt)=xmax时有3-周期点(李-约混沌);连续单峰映射f在[xmin,xt]内恰好有2个基点时,则所有基点必有下列序关系之一:xmin<…x4<x2<x0<x1<x3<x5<…<xmax或xmin<…x5<x3<x1<x0<x2<x4<…<xmax;这类连续单峰映射f具有n-周期点,若在S序中,m n,则f在[x,x]内没有周期点。

When a continuum unimodal map f satisfies f（ xmin）≤x1 and f（x1） = xmax, f has periodthree （ Li-Yorke chaos）. Whenfhas no other than two base-points in [ xmin, x1 ], all base-points series of f satisfy one of the followings：xmin〈…x4〈x2〈x0〈x1〈x3〈x5〈…〈xmax or xmin〈…x5〈x3〈x1〈x0〈x2〈x4〈…〈xmax;For these continuum unimodal maps, f has period- n. However, if m△n in Sharkovskii-series, f does not have m-periodic point in[ xmin,xmax]