传递系统的伪分解函数和应用  

PSEUDO DECOMPOSITION FUNCTION OF A TRANSITIVE SYSTEM AND APPLICATIONS

作　　者：苏勇[1] 叶向东[1] 

机构地区：[1]中国科学技术大学数学系,安徽合肥230026

出　　处：《数学年刊（A辑）》2002年第6期765-770,共6页Chinese Annals of Mathematics

基　　金：国家973计划资助的项目.

摘　　要：令X为一个紧致度量空间,f:x→X为(拓扑)传递的映射.通过对传递系统(X,f)在fn,n∈N的作用下的伪分解,先引入一个新的拓扑不变量“传递系统的PD函数(伪分解函数)”. 然后,讨论关于此不变量的一些重要性质.最后,把关于周期轨道的Sharkovskii定理推广到传递子系统上.Let X be a compact metric space and f : X → X be transitive. The authors first introduce a new topological invariant, the PD-function (pseudo decomposition function) of a transitive system, by the investigation of the pseudo decomposition of a transitive system (X,f) under the action of fn, n ∈ N. Then important properties about the invariant are discussed. Finally, Sharkovskii's theorem is generalized from periodic orbits to transitive subsystems.

关 键 词：传递性 PD函数 伪分解 Sharkovskii定理 

分 类 号：O19[理学—数学]