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Variational methods for the choreography solution to the three-body problem. (English) Zbl 1145.70314

Summary: In this paper, we give a short proof for the existence of nontrivial choreography solution to the equal-mass three-body problem, which is discovered by A. Chenciner and R. Montgomery [Ann. Math. (2) 152, No. 3, 881–901 (2000; Zbl 0987.70009)] recently.

MSC:

70F07 Three-body problems
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
70H12 Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics

Citations:

Zbl 0987.70009
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