Year: 2021
Author: Kuo-Chang Chen
Analysis in Theory and Applications, Vol. 37 (2021), Iss. 1 : pp. 24–58
Abstract
In this paper we introduce a method to construct periodic solutions for the $n$-body problem with only boundary and topological constraints. Our approach is based on some novel features of the Keplerian action functional, constraint convex optimization techniques, and variational methods. We demonstrate the strength of this method by constructing relative periodic solutions for the planar four-body problem within a special topological class, and our results hold for an open set of masses.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2021.pr80.04
Analysis in Theory and Applications, Vol. 37 (2021), Iss. 1 : pp. 24–58
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: $n$-body problem variational methods periodic solutions convex optimization.
Author Details
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Distance Estimates for Action-Minimizing Solutions of the $$N$$-Body Problem
Chen, Kuo-Chang
Pan, Bo-Yu
Regular and Chaotic Dynamics, Vol. 28 (2023), Iss. 4-5 P.561
https://doi.org/10.1134/S1560354723040044 [Citations: 0]