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Regular and Chaotic Dynamics, 2023, Volume 28, Issue 4-5, Pages 561–577
DOI: https://doi.org/10.1134/S1560354723040044 (Mi rcd1221) 		 
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.
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DOI: https://doi.org/10.1134/S1560354723040044
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.
Funding agency Grant number
Ministry of Science and Technology of Taiwan 110-2115-M-007-004-MY3
This work was supported in part by the National Science and Technology Council in Taiwan. Grant number MOST 110-2115-M-007-004-MY3.
Received: 28.02.2023
Accepted: 29.06.2023
Document Type: Article
MSC: 70F10, 70F15, 70F07
Language: English
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
Citation in format AMSBIB
\Bibitem{ChePan23}
\by Kuo-Chang Chen, Bo-Yu Pan
\paper Distance Estimates for Action-Minimizing Solutions of the $N$-Body Problem
\jour Regul. Chaotic Dyn.
\yr 2023
\vol 28
\issue 4-5
\pages 561--577
\mathnet{http://mi.mathnet.ru/rcd1221}
\crossref{https://doi.org/10.1134/S1560354723040044}
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