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

2024/07/09 by Aydin, Cengiz
#53D35 #70F10 #70G45 #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2407.06927

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-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.

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