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- W1886892306 abstract "In a preprint by Montgomery cite{Mo99}, 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 cite{CM00}). Unfortunately there is an error in the proof and the problem is still open. Consider the $alpha$-homogeneous Newton-type potential, $1/r^{alpha},$ using action minimization method, we prove the existence of this solution, for $alpha in (1,2)$; for $alpha=1$ (the Newtonian potential), an extra condition is required, which unfortunately seems hard to verify at this moment." @default.
- W1886892306 created "2016-06-24" @default.
- W1886892306 creator A5060204830 @default.
- W1886892306 date "2015-07-10" @default.
- W1886892306 modified "2023-09-26" @default.
- W1886892306 title "Shape Space Figure-$8$ Solution of Three Body Problem with Two Equal Masses" @default.
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- W1886892306 doi "https://doi.org/10.48550/arxiv.1507.02892" @default.
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