图映射的吸引中心与拓扑熵  

The Attracting Centre and the Topological Entropy of a Graph Map

作　　者：孙太祥[1,2] 席鸿建[1] 陈占和[1] 张永平[1] 

机构地区：[1]广西大学数学系 [2]中国科学技术大学数学系,合肥安徽230026

出　　处：《数学进展》2004年第5期540-546,共7页Advances in Mathematics（China）

基　　金：国家自然科学基金(10361001);广西科学基金(0447004)

摘　　要：设f是图G上的连续自映射, P(f),AΓ(f),ω(f),Ω(f),sα(y,f)分别表示f的周期点集,单侧γ-极限点集,ω-极限集,非游荡集,相对于y的特殊α-极限点集.本文证明了:(1)x∈sα(y,f)(对某个y∈G)当且仅当x∈sα(x,f);(2)AΓ(f)∪P(f)(?)∪y∈GSα(y,f);(3)AΓ(f)∪P(f)=ω(Ω(f))=ω(ω(f))=ω(∪y∈Gsα(y,f))=ω(AΓ(f)∪P(f)).此外,本文还得到了f具有正拓扑熵的几个等价条件.Let f be a continuous self-map of a graph G and P(f), AΓ(f),ω(f),Ω(f), sα(y, f) denote the set of periodic points of f, the set of unilateral γ-limit points of f, the set ofω-limit points of f, the set of nonwandering points of f, the set of special aaaaaaaaaaaaaa- limit points of f relative to y, respectively. In this paper we show that: (1) x∈?sα(y,f) for some y ∈ G if and only if x ∈ sα(x,f); (2) AΓ(f) U P(f) ∈∪y∈Gsα(y,f); (3) AΓ(f)∪ P(f) = ω(Ω(f)) = ω(ω(f)) = ω(∪y∈Gsα(y,f)) = ω(AΓ(f) ∪P(f)). Furthermore, we also obtain several equivalent conditions which f has positive topological entropy.

关 键 词：图映射 特殊α-极限点 单侧γ-极限点 拓扑熵 

分 类 号：O189.11[理学—数学]