arXiv math/06109512006-10-31math.DSmath-phmath.MP

On some exceptional cases in the integrability of the three-body problem

Alexei Tsygvintsev

备注：: 7 pages
发表信息：: Celestial Mechanics and Dynamical Astronomy, Vol. 99, No. 1, 237-247, 2007
DOI：: 10.1007/s10569-007-9086-5

英文摘要：

We consider the Newtonian planar three--body problem with positive masses $m_1$, $m_2$, $m_3$. We prove that it does not have an additional first integral meromorphic in the complex neighborhood of the parabolic Lagrangian orbit besides three exceptional cases $ \sum m_i m_j/(\sum m_k)^2= 1/3$, $2^3/3^3$, $2/3^2$ where the linearized equations are shown to be partially integrable. This result completes the non-integrability analysis of the three-body problem started in our previous papers and based of the Morales-Ramis-Ziglin approach.

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