Dendrite上无混沌群作用

The nonexistence of chaotic group actions on dendrites

称群G在紧度量空间X上的作用是混沌的,如果该作用是拓扑传递的,并且周期点集稠密.证明了当空间X是dendrite时,X上不存在混沌群作用.

The action of a group G on a compact metric space X is said to be chaotic if it is topologically transitive and has dense periodic points. We show that if X is a dendrite, then there is no chaotic group action on X.