Pointwise recurrent one-dimensional flows

摘要

Let (G, X) be a flow, where X is a graph and G is a finitely generated group. In this article, it is shown that (G, X) is a pointwise recurrent flow if and only if one of the following two statements holds: (1) X=S~1, and (G, S~1) is a minimal flow conjugate to an isometric flow, or to a finite cover of a proximal flow; (2) G is finite.