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VOL. 64 | 2015 Minimax approach to the $n$-body problem
Mitsuru Shibayama

Editor(s) Shin-Ichiro Ei, Shuichi Kawashima, Masato Kimura, Tetsu Mizumachi

## Abstract

Using the variational method Chenciner and Montgomery proved the existence of a new periodic solution of figure-eight shape to the planar three-body problem. Since then, a number of periodic solutions have been discovered as minimizers. We present a minimax approach to the $n$-body problem and prove the existence of some periodic solutions as minimax points of the action functional.

## Information

Published: 1 January 2015
First available in Project Euclid: 30 October 2018

zbMATH: 1397.70016
MathSciNet: MR3381206

Digital Object Identifier: 10.2969/aspm/06410221

Subjects:
Primary: 70F10

PROCEEDINGS ARTICLE
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Vol. 64 • 1 January 2015