Non-integrability of a Self-gravitating Riemann Liquid Ellipsoid

    2013, Volume 18, Number 5, pp.  497-507

    Author(s): Combot T.

    We consider the motion of a triaxial Riemann ellipsoid of a homogeneous liquid without angular momentum. We prove that it does not admit an additional first integral which is meromorphic in position, impulsions, and elliptic integrals which appear in the potential. This proves that the system is not integrable in the Liouville sense; we actually show that even its restriction to a fixed energy hypersurface is not integrable.
    Keywords: Morales–Ramis theory, elliptic functions, monodromy, differential Galois theory, Riemann surfaces
    Citation: Combot T., Non-integrability of a Self-gravitating Riemann Liquid Ellipsoid, Regular and Chaotic Dynamics, 2013, Volume 18, Number 5, pp. 497-507

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