I will talk about an (old) joint work with Martin Andersson about irrational torus flows with two stopping points. A straightforward computation shows that if the stopping points are of generic type, then the set of empirical measures associated to any point is included in the set of convex combinations of the Diracs on the two fixed points (this set is a segment). We show with Martin that depending on Diophantine conditions on the slope of the flow and the relative positions of the fixed points, this set will be a.e. a single point or a nontrivial segment.