Year: 2026
Type: preprint
Abstract: We prove that, for every choice of positive masses, the planar Newtonian five-body problem has finitely many central configurations up to similarity. After normalization and removal of the translation and rotation freedoms, every physical configuration is isolated in the complex solution variety. The proof combines the classification of singular sequences by Albouy and Kaloshin with a lower bound for the potential, asymptotic estimates, and local analytic reductions.
Source: arXiv (Cornell University)
Authors: Liu, Kefeng, Liu, Yangshanshan
Institution: Chongqing University of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2775328943, G504305494
OpenAlex ID: W7223119033