Suppose that φ is a nonsingular (fixed point free) C1 flow on a smooth closed 3-dimensional manifold M with H2(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.
Basener, William and Sullivan, Michael C. "Periodic Prime Knots and Toplogically transitive Flows on 3-Manifolds." (Feb 2006).