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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
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.
Received: 27.02.2023 Accepted: 20.06.2023
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
Linking options:
https://www.mathnet.ru/eng/rcd1218 https://www.mathnet.ru/eng/rcd/v28/i4/p512
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Abstract page: | 43 | References: | 24 |
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