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Journal Articles Nonlinearity Year : 2017

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

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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.

Dates and versions

insu-03718954 , version 1 (10-07-2022)

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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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