2020/11/12 by Agustín Moreno, Moreno, Agustin
Mathematics · Physics and Astronomy · #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2011.06568
openalex publication_date 2020/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.