On the finiteness of four-body central configurations

2021/03/16 by Xiang Yu, Yu, Xiang, Shuqiang Zhu +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spacecraft Dynamics and Control

paper · pdf · doi:10.48550/arxiv.2103.08906

openalex publication_date 2021/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The number of central configurations in the four body problem was proved to be finite, first by Hampton and Moeckel, then by Albouy and Kaloshin, when the masses are all positive. We prove that the four-body central configurations are finite for any four nonzero masses.

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