树映射的稠密混沌(英文)

Dense chaos for tree maps

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.