Pseudo-holomorphic dynamics in the restricted three-body problem
Abstract
In this article, we identify the 5-dimensional analogue of the finite energy foliations introduced by Hofer--Wysocki--Zehnder for the study of 3-dimensional Reeb flows, and show that these exist for the spatial circular restricted three-body problem (SCR3BP) whenever the planar dynamics is convex. We introduce the notion of a fiberwise-recurrent point, which may be thought of as a symplectic version of the leafwise intersections introduced by Moser, and show that they exist in abundance for a perturbative regime in the SCR3BP. We then use this foliation to induce a Reeb flow on the standard 3-sphere, via the use of pseudo-holomorphic curves, to be understood as the best approximation of the given dynamics that preserves the foliation. We discuss examples, further geometric structures, and speculate on possible applications.
Keywords
Cite
@article{arxiv.2011.06568,
title = {Pseudo-holomorphic dynamics in the restricted three-body problem},
author = {Agustin Moreno},
journal= {arXiv preprint arXiv:2011.06568},
year = {2022}
}
Comments
v3: changed abstract, improved presentation in the intro, added appendix on curious examples of Lorentz metrics and open books. To appear in Math. Proc. of the Cam. Phil. Soc