拓扑动力系统中渐近周期点的存在性  

Existence of the Asymptotic Periodic Point in the Topological Dynamics System

作　　者：林银河[1] 

机构地区：[1]丽水学院数理学院

出　　处：《河北大学学报（自然科学版）》2007年第4期345-348,共4页Journal of Hebei University(Natural Science Edition)

基　　金：浙江省自然科学基金资助项目(M103069);重庆市教委科学研究项目(05JWSK054);丽水学院重点项目(FZ070015)

摘　　要：设(X,f)是一个拓扑动力系统,S是X的子集.本文首先讨论了若S为f的混沌集,则f在S内至多只有1个渐近周期点;若S为f的混沌集并且f(S)是S的子集及f所有周期点的周期都大于1,则f在S内不存在渐近周期点.然后研究了f在一般集合S内是否存在渐近周期点的条件.得到了如果当S的闭包和f的周期点集不相交且f(S)是S的子集,则f在S内不存在渐近周期点;如果存在S的f正半轨道中的某一项和f的周期点集相交,则f在S内存在渐近周期点.If （X, f） is a topological dynamics system, S is a subset of X. In this paper, it first discusses that if f has the chaotic set S, then f has no more than one asymptotic periodic point in S. Meanwhile, if S is a chaotic set of f, f（S） is a subset of S and every period of all periodic points of f is more bigger than one, then f doesn＇ t have asymptotic periodic point in S. After that it studies the condition that f has or doesn＇t have the asymptotic periodic point in the ordinary set S and obtain if the closure of S doesn＇t intersect with the set of all periodic points d f and f（S ） is a subset of S, then f doesn＇ t exist asymptotic periodic point in S ; if there is a term in the positive orbit of S about f, which intersects with the set of all periodic points of f, then f exists asymptotic periodic point in S.

关 键 词：混沌集 周期点 渐近周期点 

分 类 号：O193[理学—数学]