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arXiv · 2301.02305

Smale's 6th problem for generic masses

Anders N. Jensen·Anton Leykin
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Abstract

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.

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Anders N. Jensen, Anton Leykin. 2023-01-05. Smale's 6th problem for generic masses. https://arxiv.org/abs/2301.02305

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