关于逐点伪轨跟踪性的研究  

Research on Pointwise Pseudo-orbit Tracing Property

作　　者：黎日松[1] 吴华明[2] 

机构地区：[1]广东海洋大学理学院,广东湛江524025 [2]湛江师范学院数学与计算学院,广东湛江524048

出　　处：《广东海洋大学学报》2007年第1期64-68,共5页Journal of Guangdong Ocean University

摘　　要：设X和～X为度量空间,且X是紧致的,f是X上连续自映射,证明了:若fk有PWPOTP(PWPOTP+),则f有PWPOTP(PWPOTP+);满射f有PWPOTP(PWPOTP+)当且仅当由(X,f)生成的逆极限系统(Xf,σf)上转移自映射σf有PWPOTP(PWPOTP+);PWPOTP(PWPOTP+)是拓扑共轭不变性;设f,g分别为X～和X上自同胚(自映射),π∶～X→X为局部等距覆盖映射,且πf=gπ,若有δ0>0,使对x～∈～X和δ>0(δ≤δ0),x～的半径为δ的开球Uδ(x～)连通,且πUδ(x～)为等距映射,则f有PWPOTP(PWPOTP+)当且仅当g有PWPOTP(PWPOTP+);恒等映射id有PWPOTP当且仅当X是完全不连通的。Let X and X^- be metric spaces and X be compact, and let f be a continuous map from X to itself. In this paper, the following statements were proved： If f^K has PWPOTP（PWPOTP＋ ）, then f has PWPOTP （PWPOTP＋） ;Let f be a surjection and （ Xf, df） be the inverse limit space generated by （ X ,f）, and σf be the shift map on Xf. then f has PWPOTP（ PWPOTP＋ ）if and only if σf has PWPOTP（ PWPOTP＋ ）; PWPOTP （PWPOTP ＋ ）is an invariant property under topological conjugation;Let f： X→ X and g： X^→ X^- be homeomorphisms （continuous maps）, and π： X^→ X be a locally isometric covering map such that π°f= g°π. If there exists δ0 〉 0 such that for each x^-∈ X^- and δ 〉 0（ δ≤δ0） the open ball Uδ（x^-） of x^- with radius δ is connected and π｜ Uδ（x^-） is an isometry,then f has PWPOTP（PWPOTP＋ ） if and only if g has PWPOTP（PWPOTP＋ ）; The identity map id has PWPOTP if and only if X is totally disconnected.

关 键 词：伪轨跟踪性 逐点伪轨跟踪性 链可迁 

分 类 号：O175.1[理学—数学]