Geodesic
The Euler--Jacobi--Lie integrability theorem
Russian journal of nonlinear dynamics, Tome 9 (2013) no. 2, pp. 229-245

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This paper addresses a class of problems associated with the conditions for exact integrability of a system of ordinary differential equations expressed in terms of the properties of tensor invariants. The general theorem of integrability of the system of $n$ differential equations is proved, which admits $n-2$ independent symmetry fields and an invariant volume $n$-form (integral invariant). General results are applied to the study of steady motions of a continuous medium with infinite conductivity.
Keywords: symmetry field, integral invariant, nilpotent group, magnetic hydrodynamics. 
@article{ND_2013_9_2_a2,
     author = {Valery V. Kozlov},
     title = {The {Euler--Jacobi--Lie} integrability theorem},
     journal = {Russian journal of nonlinear dynamics},
     pages = {229--245},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2013_9_2_a2/}
}
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Valery V. Kozlov. The Euler--Jacobi--Lie integrability theorem. Russian journal of nonlinear dynamics, Tome 9 (2013) no. 2, pp. 229-245. http://geodesic.mathdoc.fr/item/ND_2013_9_2_a2/