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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{liu2026finiteness,
  title = {{Finiteness of Dziobek central configurations in the Newtonian five-body problem}},
  author = {Kefeng Liu and Yangshanshan Liu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32751},
  eprint = {2610.32751},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32751},
}
RIS
TY  - UNPB
TI  - Finiteness of Dziobek central configurations in the Newtonian five-body problem
AU  - Kefeng Liu
AU  - Yangshanshan Liu
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32751
UR  - https://arxiv.org/abs/2610.32751
AB  - 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.
ER  -