Dendrite Flows

Let (G, D) be a flow such that D is a dendrite and G is a finitely generated group. Denote by E(D) the set of endpoints of D. In this paper, it is shown that if E(D) is closed and countable then the following properties are equivalent: (1) (G, D) is pointwise periodic; (2) (G, D) is pointwise almost periodic; (3) The orbit closure relation is closed; (4) (G, D) is equicontinuous. In addition, we show that if E(D) is countable, then (G, D) is not a minimal flow. We also show that if (G, D) is a pointwise periodic flow and if D does not contain any homeomorphic copy of special dendrites, then the action of G can factor through a finite group action.