  When the planar circular restricted 3-body problem (RTBP) is periodically
perturbed, families of unstable periodic orbits break up into whiskered tori,
with most tori persisting into the perturbed system. In this study, we 1)
develop a quasi-Newton method which simultaneously solves for the tori and
their center, stable, and unstable directions; 2) implement continuation by
both perturbation as well as rotation numbers; 3) compute Fourier-Taylor
parameterizations of the stable and unstable manifolds; 4) regularize the
equations of motion; and 5) globalize these manifolds. Our methodology improves
on efficiency and accuracy compared to prior studies, and applies to a variety
of periodic perturbations. We demonstrate the tools near resonances in the
planar elliptic RTBP.
