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Regular and Chaotic Dynamics, 2023, Volume 28, Issue 4-5, Pages 512–532
DOI: https://doi.org/10.1134/S1560354723520076
(Mi rcd1218)
 

Special Issue: On the 80th birthday of professor A. Chenciner

On the Uniqueness of Convex Central Configurations in the Planar 4-Body Problem

Shanzhong Suna, Zhifu Xieb, Peng Youc

a Department of Mathematics; Academy for Multidisciplinary Studies, Capital Normal University, 100048 Beijing, P. R. China
b School of Mathematics and Natural Science, The University of Southern Mississippi, MS 39406 Hattiesburg, USA
c School of Mathematics and Statistics, Hebei University of Economics and Business, 050061 Shijiazhuang Hebei, P. R. China
References:
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 2020YFA 0713300
National Natural Science Foundation of China 11771303
12171327
11911530092
12261131498
11871045
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.
Received: 27.02.2023
Accepted: 20.06.2023
Document Type: Article
MSC: 70F10, 70F15
Language: English
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
Citation in format AMSBIB
\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}
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    References:24
     
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