Regular and Chaotic Dynamics

, Volume 18, Issue 5, pp 497–507 | Cite as

Non-integrability of a self-gravitating riemann liquid ellipsoid

Article

Abstract

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 

MSC2010 numbers

37J30 

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Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.IMCCEParisFrance

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