The Size of Ghost Rods
Résumé
"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 sire of ghost; rods; that is, the magnitude of their impact on material lines.