Auslander-yorke Chaos For Group Actions On Dendrites

In this paper, we discuss Auslander-Yorke chaos and sensitivity of group actionson dendrites. First, we show that each sensitive group action on a dendrite contains anAuslander-Yorke chaotic subsystem. By this conclusion, we prove that each sensitivegroup action on a dendrite must have a ping-pong game, which implies that eachsensitive fnitely generated group action on a dendrite has positive geometric entropy,and each dendrite admits no sensitive nilpotent group actions. At last, we constructtwo examples: a sensitive but non-expansive slovable group action on a dendrite, and asensitive group action on a ring domain without an Auslander-Yorke chaotic subsystem.