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Rose solutions with three petals for planar 4-body problems. (English) Zbl 1371.70036

Summary: For planar Newtonian 4-body problems with equal masses, we use variational methods to prove the existence of a non-collision periodic choreography solution such that all bodies move on a rose-type curve with three petals.

MSC:

70F10 \(n\)-body problems
70H12 Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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References:

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