Rapid and Accurate Methods for Computing Whiskered Tori and their Manifolds in Periodically Perturbed Planar Circular Restricted 3-Body Problems. (arXiv:2105.11100v3 [math.DS] UPDATED)
<a href="http://arxiv.org/find/math/1/au:+Kumar_B/0/1/0/all/0/1">Bhanu Kumar</a>, <a href="http://arxiv.org/find/math/1/au:+Anderson_R/0/1/0/all/0/1">Rodney L. Anderson</a>, <a href="http://arxiv.org/find/math/1/au:+Llave_R/0/1/0/all/0/1">Rafael de la Llave</a>
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.
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.
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