Contact geometry of Hill's approximation in a spatial restricted four-body problem
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909541184045056 |
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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 |