拓扑动力系统中渐近周期点的存在性

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.

Existence of the Asymptotic Periodic Point in the Topological Dynamics System

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 of 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.