中文摘要：

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）≠0。

英文摘要：

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.