Contact geometry of Hill's approximation in a spatial restricted four-body problem

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1. Verfasser: Aydin, Cengiz
Format: Preprint
Veröffentlicht: 2024
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author Aydin, Cengiz
author_facet Aydin, Cengiz
contents 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-García 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.
format Preprint
id arxiv_https___arxiv_org_abs_2407_06927
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Contact geometry of Hill's approximation in a spatial restricted four-body problem
Aydin, Cengiz
Symplectic Geometry
Dynamical Systems
70G45, 70F10, 53D35
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-García 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.
title Contact geometry of Hill's approximation in a spatial restricted four-body problem
topic Symplectic Geometry
Dynamical Systems
70G45, 70F10, 53D35
url https://arxiv.org/abs/2407.06927