  'Ghost Rods' are periodic structures in a two-dimensional flow that have an
effect on material lines that is similar to real stirring rods. An example is a
periodic island: material lines exterior to it must wrap around such an island,
because determinism forbids them from crossing through it. Hence, islands act
as topological obstacles to material lines, just like physical rods, and lower
bounds on the rate of stretching of material lines can be deduced from the
motion of islands and rods. Here, we show that unstable periodic orbits can
also act as ghost rods, as long as material lines can 'fold' around the orbit,
which requires the orbit to be parabolic. We investigate the factors that
determine the effective size of ghost rods, that is, the magnitude of their
impact on material lines.
