  For Reeb vector fields on closed 3-manifolds, cylindrical contact homology is
used to show that the existence of a set of closed Reeb orbit with certain
knotting/linking properties implies the existence of other Reeb orbits with
other knotting/linking properties relative to the original set. We work out a
few examples on the 3-sphere to illustrate the theory, and describe an
application to closed geodesics on $S^2$ (a version of a result due to
Angenent).
