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Minimax approach to the $$n$$-body problem. (English) Zbl 1397.70016
Ei, Shin-Ichiro (ed.) et al., Nonlinear dynamics in partial differential equations. Proceedings of the 4th MSJ-SI international conference, Kyushu, Japan, September 12–21, 2011. Tokyo: Mathematical Society of Japan (ISBN 978-4-86497-022-8/hbk). Advanced Studies in Pure Mathematics 64, 221-228 (2015).
Summary: Using the variational method A. Chenciner and R. Montgomery [Ann. Math. (2) 152, No. 3, 881–901 (2000; Zbl 0987.70009)] 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.
For the entire collection see [Zbl 1321.35002].
MSC:
 70F10 $$n$$-body problems
Keywords:
choreography; variational method
Zbl 0987.70009