Regular and Chaotic Dynamics

, Volume 18, Issue 5, pp 497–507

Non-integrability of a self-gravitating riemann liquid ellipsoid


DOI: 10.1134/S1560354713050031

Cite this article as:
Combot, T. Regul. Chaot. Dyn. (2013) 18: 497. doi:10.1134/S1560354713050031


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.


Morales-Ramis theory elliptic functions monodromy differential Galois theory Riemann surfaces 

MSC2010 numbers


Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.IMCCEParisFrance

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