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PreprintarXiv licencearXiv

Finiteness of planar central configurations of five bodies with positive masses

  • Kefeng Liu
  • Yangshanshan Liu
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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.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026finiteness,
  title = {{Finiteness of planar central configurations of five bodies with positive masses}},
  author = {Kefeng Liu and Yangshanshan Liu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28168},
  eprint = {2610.28168},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28168},
}
RIS
TY  - UNPB
TI  - Finiteness of planar central configurations of five bodies with positive masses
AU  - Kefeng Liu
AU  - Yangshanshan Liu
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28168
UR  - https://arxiv.org/abs/2610.28168
AB  - 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.
ER  -