On invariant manifolds attached to oscillating boundaries in Stokes flows

Consider a steady Stokes flow bounded by a flat wall to which a separatrix, not tangent to the wall, is attached at point S. If the wall is made to slowly oscillate periodically with small amplitude in a longitudinal direction, then the Poincare map associated with this perturbed flow has a fixed point on the wall near S with an invariant manifold. This result also holds for flows bounded by a cylindrical wall and flows in which the small periodic perturbation is not due to the oscillation of the wall. This result is applied to several flow geometries in the literature. (c) 1997 American Institute of Physics.