TOPOLOGICAL ANGLES NEAR A PERIODIC ORBIT

We show that a purely classical phase lag (or advance) is associated w ith homoclinic motion near a periodic orbit. Trajectories which leave the separatrix region belonging to a given unstable periodic orbit ret urn with a phase shift relative to the periodic orbit, at fixed energy . The phase is topological in that it counts the number of homoclinic cycles but is insensitive to how long it takes to make them.