Knots and topologically transitive flows on 3-manifolds
Abstract
Suppose that () 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 = S^3, 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 (Refer to PDF file for exact formulas).