Knots and topologically transitive flows on 3-manifolds

Suppose that ϕ is a nonsingular (fixed point free) flow on a smooth three-dimensional manifold M. Suppose the orbit though a point p∈M is dense in M. Let D be an imbedded disk in M containing p which is transverse to the flow. Suppose that q∈D is a point in the forward orbit of p. Under certain assumptions on M, which include the case M=S3, we prove that if q is sufficiently close to p then the orbit segment from p to q together with a compact segment in D from p to q forms a nontrivial prime knot in M.