Abstract
Let (G, X) be a flow such that X is a locally finite graph and G is a finitely generated group. In this paper, it is shown that the following properties are equivalent:
1. (G, X) is pointwise recurrent;
2. (G, X) is pointwise periodic;
3. (G, X) is pointwise almost periodic.
We show that every pointwise recurrent flow of a locally finite graph is equicontinuous. We also give some qualitative properties of an equicontinuous flow.