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Shape space figure-8 solution of three body problem with two equal masses

Abstract : In a preprint by Montgomery (https://people.ucsc.edu/~rmont/Nbdy.html), the author attempted to prove the existence of a shape space figure-8 solution of the Newtonian three body problem with two equal masses (it looks like a figure 8 in the shape space, which is different from the famous figure-8 solution with three equal masses (Chenciner and Montgomery 2000 Ann. Math. 152 881-901)). Unfortunately there is an error in the proof and the problem is still open.

Consider the α-homogeneous Newton-type potential, 1/rα, using action minimization method, we prove the existence of this solution, for α \in (1, 2) ; for α=1 (the Newtonian potential), an extra condition is required, which unfortunately seems hard to verify at this moment.

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https://hal-insu.archives-ouvertes.fr/insu-03718954
Contributor : Nathalie POTHIER Connect in order to contact the contributor
Submitted on : Sunday, July 10, 2022 - 11:06:57 AM
Last modification on : Wednesday, August 3, 2022 - 3:58:40 AM

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Guowei Yu. Shape space figure-8 solution of three body problem with two equal masses. NONLINEARITY, 2017, 30, pp.2279. ⟨10.1088/1361-6544/aa6ab0⟩. ⟨insu-03718954⟩

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