Periodic prime knots and topologically transitive flows on 3-manifolds

Suppose that φ is a nonsingular (fixed point free) C 1 flow on a smooth closed 3-dimensional manifold M with H 2 ( M ) = 0 . Suppose that φ has a dense orbit. We show that there exists an open dense set N ⊆ M such that any knotted periodic orbit which intersects N is a nontrivial prime knot.