21-28 Bhanu Kumar, Rodney L. Anderson, Rafael de la Llave
Rapid and Accurate Computation of Whiskered Tori and their Manifolds Near Resonances in Periodically Perturbed Planar Circular Restricted 3-Body Problems (3744K, LaTeX 2e) May 24, 21
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Abstract. When the planar circular restricted 3-body problem (RTBP) is periodically perturbed, families of unstable resonant 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 on the planar elliptic RTBP.

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