Kuo-Chang Chen

Address: 101 Sec 2, Kuanfu Rd, Hsinchu 300, Taiwan

E-mail: kchen@math.nthu.edu.tw

University: National Tsing Hua University

Publications:

Chen K., Pan B.

Distance Estimates for Action-Minimizing Solutions of the $N$-Body Problem
2023, vol. 28, nos. 4-5, pp. 561-577

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 actionminimizing solutions for three- and four-body problems.

Keywords: $N$-body problem, variational method, mutual distance

Citation: Chen K., Pan B., Distance Estimates for Action-Minimizing Solutions of the $N$-Body Problem, Regular and Chaotic Dynamics, 2023, vol. 28, nos. 4-5, pp. 561-577

DOI:10.1134/S1560354723040044

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