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The meromorphic non-integrability of the three-body problem

Alexei Tsygvintsev
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Abstract

We study the planar three-body problem and prove the absence of a complete set of complex meromorphic first integrals in a neighborhood of the Lagrangian solution. We use the Ziglin's method and study the monodromy group of the corresponding normal variational equations.

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Alexei Tsygvintsev. 2000-09-25. The meromorphic non-integrability of the three-body problem. https://arxiv.org/abs/math/0009218

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