Contact geometry of Hill's approximation in a spatial restricted four-body problem
Symplectic Geometry
2025-03-19 v2 Dynamical Systems
Abstract
It is well-known that the planar and spatial circular restricted three-body problem (CR3BP) is of contact type for all energy values below the first critical value. Burgos-Garc\'ia and Gidea extended Hill's approach in the CR3BP to the spatial equilateral CR4BP, which can be used to approximate the dynamics of a small body near a Trojan asteroid of a Sun--planet system. Our main result in this paper is that this Hill four-body system also has the contact property. In other words, we can "contact" the Trojan. Such a result enables to use holomorphic curve techniques and Floer theoretical tools in this dynamical system in the energy range where the contact property holds.
Keywords
Cite
@article{arxiv.2407.06927,
title = {Contact geometry of Hill's approximation in a spatial restricted four-body problem},
author = {Cengiz Aydin},
journal= {arXiv preprint arXiv:2407.06927},
year = {2025}
}