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arXiv · 2610.32751

Finiteness of Dziobek central configurations in the Newtonian five-body problem

Kefeng Liu·Yangshanshan Liu
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Abstract

We prove that, for any five fixed strictly positive masses, the Newtonian central configurations of exact affine dimension three form finitely many similarity classes. The proof uses the Dziobek equations, two constant identities, and local analysis of zeros and poles on a compact complex curve.

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Kefeng Liu, Yangshanshan Liu. 2026-10-23. Finiteness of Dziobek central configurations in the Newtonian five-body problem. https://arxiv.org/abs/2610.32751

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