Exact classification of nondegenerate divergence-free vector fields on surfaces of small genus (Q1569774)

The paper deals with the classification up to conjugation in \(C^k\), \(k = 1,\dots,\infty,\) of complete nondegenerate divergence-free vector fields on compact connected two-dimensional manifolds (possibly with boundary) almost all of whose trajectories are closed. The author solves the problem of classification up to conjugation for nondegenerate divergence-free vector fields on the sphere, the projective plane, the Klein bottle, the torus, and the torus with Möbius band pasted in, possibly with several disks removed.