树映射的稠密混沌(英文)  

Dense chaos for tree maps

作　　者：庞琳娜[1] 张更容[1] 曾凡平[2] 

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004 [2]柳州师范高等专科学校,广西柳州545004

出　　处：《柳州师专学报》2007年第3期103-109,共7页Journal of Liuzhou Teachers College

基　　金：Project supported by the Natural Science Foundation of China(10661001),Guangxi Science Foundation(0249002,0007002)and Innovation Pro-ject of Guangxi Graduate Education(2006105930701 M14).

摘　　要：设T是树,f∶T→T是连续映射。在本文我们显示下列性质等价:(1)f是通用混沌,(2)对某个δ>0,f是通用δ-混沌,(3)对某个δ>0,f是稠密δ-混沌,(4)或者存在唯一的传递的非退化的连通闭集,或者存在k(k 2)个有公共端站的传递的非退化的连通闭集;且如果J是非退化的连通集合,则f(J)是非退化的,且存在传递的连通集合I0和整数n使得fn(J)∩Int(I0)≠。Let T be a tree and f： T→T be a continuous map. In this paper, we show that the following four conditions are equivalent： （1）f is generically chaotic;（2）f is generically δ-chaotic for some δ 〉 0; （3）f is denny δ-chaotic for some δ 〉 0; （4） either there exists a unique transitive closed non degenerate connected set or there exist k （ k ≥2 ） transitive closed non degenerate connected components having a common endpoint; naoreover, if J is a non degenerate connected set then f（J） is non degenerate,and there exist a transitive connected set Io and an integer n such that fn（J） ∩ Int（Io）≠0.

关 键 词：拓扑传递 拓扑混合 通用混沌 稠密δ-混沌 

分 类 号：O415.5[理学—理论物理]