Rapid and Accurate Computation of Invariant Tori, Manifolds, and Connections Near Mean Motion Resonances in Periodically Perturbed Planar Circular Restricted 3-Body Problem Models

CDSNS Colloquium
Wednesday, July 8, 2020 - 12:00pm for 1 hour (actually 50 minutes)
Bluejeans: https://primetime.bluejeans.com/a2m/live-event/xsgxxwbh
Bhanu Kumar – Georgia Tech – bkumar30@gatech.edu
Alex Blumenthal

When the planar circular restricted 3-body problem (RTBP) is periodically perturbed, most unstable resonant periodic orbits become invariant tori. 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 parameter as well as rotation numbers; 3) compute Fourier-Taylor parameterizations of the stable and unstable manifolds; 4) globalize these manifolds; and 5) compute homoclinic and heteroclinic connections. Our methodology improves on efficiency and accuracy compared to prior studies, and applies to a variety of periodic perturbations. We demonstrate the tools on the planar elliptic RTBP. This is based on joint work with R. Anderson and R. de la Llave.