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Existence of quasi-periodic solutions to the three-body problem

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Abstract

A rigorous proof is given for the existence of quasi-periodic solutions with only two degrees of freedom to a planar three-body problem. The solution corresponds physically to the small bodies moving on different, nearly elliptical orbits about a large mass located at a focus. The perihelia of the two orbits are locked in such a way that the difference of the two perihelia has mean value zero.

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  1. Dept. of Math., Polytechnic Institute of Brooklyn, 11201, Brooklyn, N.Y., USA

    Burton B. Lieberman

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  1. Burton B. Lieberman
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Lieberman, B.B. Existence of quasi-periodic solutions to the three-body problem. Celestial Mechanics 3, 408–426 (1971). https://doi.org/10.1007/BF01227790

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  • DOI: https://doi.org/10.1007/BF01227790

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