树映射的ω-极限集与湍流  

ω-Limit Sets and Turbulent of Tree Maps

作　　者：孙太祥[1] 

机构地区：[1]汕头大学数学所

出　　处：《数学学报（中文版）》2002年第2期253-260,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(19961001);广西科学基金资助项目(0135027)

摘　　要：设Ｔ是个树，ｆ：Ｔ→Ｔ是个连续自映射，　ｎ是Ｔ的端点数，ｘ∈Ｔ．本文证明：（１）如果存在ｚ∈ω（ｘ，ｆ）∩Ｆ（ｆ），使ｚ是ω（ｘ，ｆ）的一个单侧聚点，那么一定存在ｒ∈Ｎｎ－１，使ｆｒ含有湍流；（２）如果ω（ｘ，ｆ）是个含有不动点的无穷集，那么必存在ｒ∈Ｎｎ，使ｆｒ含有湍流．Let T be a tree, f: T → T be a continuous self-map, n be the number of the end points of T, and x ∈ T. In this paper, we prove that: (1) if there exists z ∈ ω(x, f) ∩ F(f) such that z is an unilateral accumulation point of ω(x, f), then there etists r ∈ Nn-1 such that fr has turbulent, (2) if ω(x, f) is an infinite set having the fixed points, then there exists r ∈ Nn such that fr has turbulent.

关 键 词：树映射 单侧聚点 Ω-极限集 湍流 拓扑熵 动力学性质 

分 类 号：O189.11[理学—数学]