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Special Issue: On the 80th birthday of professor A. Chenciner
Distance Estimates for Action-Minimizing Solutions of the $N$-Body Problem
Kuo-Chang Chena, Bo-Yu Panb a Department of Mathematics, National Tsing Hua University,
101, Sec 2, Kuangfu Rd., 300 Hsinchu, Taiwan R.O.C.
b Department of Applied Mathematics, National Chung Hsing University,
145 Xingda Rd., South Dist., 402 Taichung, Taiwan R.O.C.
Abstract:
In this paper we provide estimates for mutual distances of periodic solutions
for the Newtonian $N$-body problem. Our estimates are based on masses, total variations of
turning angles for relative positions, and predetermined upper bounds for action values. Explicit
formulae will be proved by iterative arguments. We demonstrate some applications to action-minimizing solutions for three- and four-body problems.
Keywords:
$N$-body problem, variational method, mutual distance.
Received: 28.02.2023 Accepted: 29.06.2023
Citation:
Kuo-Chang Chen, Bo-Yu Pan, “Distance Estimates for Action-Minimizing Solutions of the $N$-Body Problem”, Regul. Chaotic Dyn., 28:4-5 (2023), 561–577
Linking options:
https://www.mathnet.ru/eng/rcd1221 https://www.mathnet.ru/eng/rcd/v28/i4/p561
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Abstract page: | 37 | References: | 20 |
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