Smale's 6th problem for generic masses
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916893088022528 |
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| author | Jensen, Anders N. Leykin, Anton |
| author_facet | Jensen, Anders N. Leykin, Anton |
| contents | We give a new method to attempt to prove that, for a given $n$, there are finitely many equivalence classes of planar central configurations in the Newtonian $n$-body problem for generic masses.
The human part of the proof relies on tropical geometry. The crux of our technique is in a computation that we have completed for $n\leq 5$, thus confirming the celebrated result of Albouy and Kaloshin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_02305 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Smale's 6th problem for generic masses Jensen, Anders N. Leykin, Anton Algebraic Geometry Dynamical Systems 70F15 (Primary) 14T90, 14Qxx (Secondary) We give a new method to attempt to prove that, for a given $n$, there are finitely many equivalence classes of planar central configurations in the Newtonian $n$-body problem for generic masses. The human part of the proof relies on tropical geometry. The crux of our technique is in a computation that we have completed for $n\leq 5$, thus confirming the celebrated result of Albouy and Kaloshin. |
| title | Smale's 6th problem for generic masses |
| topic | Algebraic Geometry Dynamical Systems 70F15 (Primary) 14T90, 14Qxx (Secondary) |
| url | https://arxiv.org/abs/2301.02305 |