DYNAMICS OF CONTINUUM-WISE-EXPANSIVE GROUP ACTIONS ON CIRCLE

The notion of expansive group action is important in topological dynamics and continuum theory. In this paper a new group action will be introduced and studied, namely the continuum-wise-expansive group action. It is shown that each continuum-wise-expansive group action, ϕ : G S1 ! S1, has a ping pong game, and has positive geometry entropy when the action group is nitely generated. As a corollary, it is shown that unit circle admits no continuum-wise-expansive nilpotent group actions