链可迁映射

CHAIN TRANSITIVE MAPS

本文讨论紧致度量空间 X 上的链可迁自映射 f,主要证明了:1.f 不是链可迁的充要条件是存在非空开集 U,使(?)X 且 f((?))(?)U。2.若满射 f 的ω极限集含于 f 的一个链分支(链混合分支)之中,则 f 在 X 上是链可迁(链混合)的。3.若 X=S^1或 I(=[0,1]),f 是链可迁的且具有伪轨道跟踪性质,则 f 敏感依赖于初始条件且在 X 上的强混沌的。4.若X=S^1或 I 且 f 为满射,如 Γ((f)=(?)(ω(x,f)∩α(x,f))含于 f 的一个链分支(链混合分支)之中,则 f 在 X 上是链可迁(链混合)的,若Γ(f)连通,则 f 在 X 上链混合的。

In this paper,We study the Chain transitive self-maps f of Compact metricspace X.The following theorems are proved:1.f is not chain transitive iffthere is an open Set U≠φ,X≠(?) and f(?)(?)U_o 2.If W(f)=(?)ω(x,f)isContained in a Chain Component(chain mixing Camponent)of f and f is onto,then f is transitive(chaim mixing)on X.3.If X=s^1或I=[0,1],f is Chaintransitive and f has the pseudo—orbit tracing property,then f is sensitive toinitial Conditions and f is strongly Chaotic[12] on X.4.Let X=s^1 or I and fis onto,ifΓ(f)=(?)(ω(x,f)∩a(x,f))is Contained in a Chain Component(Chainmixing Component)of f,then f is Chain transitive(Chain mixing)On X.Suppose Γ(f)is Connected,then f is Chain mixing on X.