Using GPUs and the Parameterization Method for Rapid Search and
Refinement of Connections between Tori in Periodically Perturbed Planar
Circular Restricted 3-Body Problems
When the planar circular restricted 3-body problem is periodically perturbed,
most unstable periodic orbits become invariant tori. However, 2D Poincar\'e
sections no longer work to find their manifolds' intersections; new methods are
needed. In this study, we first review a method of restricting the intersection
search to only certain manifold subsets. We then implement this search using
Julia and OpenCL, representing the manifolds as triangular meshes and gaining a
30x speedup using GPUs. We finally show how to use manifold parameterizations
to refine the approximate connections found in the mesh search. We demonstrate
the tools on the planar elliptic RTBP.Comment: 20 pages, 6 figure