This article is cited in 2 papers

Non-integrability of a Self-gravitating Riemann Liquid Ellipsoid

Thierry Combot

IMCCE, 77 Avenue Denfert-Rochereau, 75014 Paris

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.

MSC: 37J30

Received: 23.09.2011
Accepted: 07.09.2013

Language: English

DOI: 10.1134/S1560354713050031

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