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JOURNALS // Regular and Chaotic Dynamics // Archive

Regul. Chaotic Dyn., 2023 Volume 28, Issue 4-5, Pages 561–577 (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.

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.

MSC: 70F10, 70F15, 70F07

Received: 28.02.2023
Accepted: 29.06.2023

Language: English

DOI: 10.1134/S1560354723040044



© Steklov Math. Inst. of RAS, 2024