Abstract:
In this paper, we provide a rigorous computer-assisted proof (CAP) of the conjec-
ture that in the planar four-body problem there exists a unique convex central configuration for
any four fixed positive masses in a given order belonging to a closed domain in the mass space.
The proof employs the Krawczyk operator and the implicit function theorem (IFT). Notably,
we demonstrate that the implicit function theorem can be combined with interval analysis,
enabling us to estimate the size of the region where the implicit function exists and extend our
findings from one mass point to its neighborhood.
Keywords:
central configuration, convex central configuration, uniqueness, N-body problem,
Krawczyk operator, implicit function theorem.
Funding agency
Grant number
National Key Research and Development Program of China
Shanzhong Sun is partially supported by the National Key R&D Program of China (2020YFA
0713300), NSFC (Nos. 11771303, 12171327, 11911530092, 12261131498, 11871045). Zhifu Xie is
partially supported by Wright W. and Annie Rea Cross Endowment Funds at the University of
Southern Mississippi.
Citation:
Shanzhong Sun, Zhifu Xie, Peng You, “On the Uniqueness of Convex Central Configurations
in the Planar 4-Body Problem”, Regul. Chaotic Dyn., 28:4-5 (2023), 512–532
\Bibitem{SunXieYou23}
\by Shanzhong Sun, Zhifu Xie, Peng You
\paper On the Uniqueness of Convex Central Configurations
in the Planar 4-Body Problem
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 4-5
\pages 512--532
\mathnet{http://mi.mathnet.ru/rcd1218}
\crossref{https://doi.org/10.1134/S1560354723520076}
Linking options:
https://www.mathnet.ru/eng/rcd1218
https://www.mathnet.ru/eng/rcd/v28/i4/p512
This publication is cited in the following 2 articles:
Alanna Hoyer-Leitzel, Phuong Le, “Symmetric Relative Equilibria with One Dominant and Four Infinitesimal Point Vortices”, J Dyn Diff Equat, 2025
Yangshanshan Liu, Shiqing Zhang, “A characterization of a special planar 5-body central configuration with a trapezoidal convex hull”, Journal of Geometry and Physics, 213 (2025), 105494
Citation in format AMSBIB
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