Non-Wandering Flows on the 2-Manifolds

Let ω be a closed 1-form on a compact surface M. A non-wandering flow on M is given by the vector field v whose inner product ivω is again a closed 1-form. For such flows we establish a topological invariant which is a graph endowed with the rotation and the weight functions. It is shown that this graph is a discrete invariant which classifies the non-wandering flows. Conversely, for an abstractly given set of such invariants we solve a realization problem