Non integrability of a self-gravitating Riemann liquid ellipsoid

Details Non integrability of a self-gravitating Riemann liquid ellipsoid Non integrability of a self-gravitating Riemann liquid ellipsoid

2012-02-08

arxiv.org/abs/1202.1771v1

Mathematics

Dynamical Systems

14 pages, 8 references

Scientific paper

We prove that the motion of a triaxial Riemann ellipsoid of homogeneous
liquid without angular momentum does not possess an additional first integral
which is meromorphic in position, impulsions, and the elliptic functions which
appear in the potential, and thus is not integrable. We prove moreover that
this system is not integrable even on a fixed energy level hypersurface.

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