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On tensor invariants of dynamical systems on three-dimensional manifolds
Theoretical and applied mechanics, Tome 20 (1994) no. 1, p. 119 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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We consider dynamical systems on compact threedimensional manifolds which have an invariant volume form. An important example is given by Hamilton equations of a system with two degrees of freedom restricted to three-dimensional lever surface of the energy integral. In this system we study the existence of tensor invariants (a first integral, a symmetry field, an invariant form) and give conditions of integrability by quadratures under the existence of a tensor invariant. We show that the infinite number of nondegenerate periodic trajectories and spliting of separatices obstruct the existence of nontrivial integral invariants analytical on the three-dimensional manifeld 
@article{TAM_1994_20_1_a9,
     author = {V. V. Kozlov},
     title = {On tensor invariants of dynamical systems on three-dimensional manifolds},
     journal = {Theoretical and applied mechanics},
     pages = {119 },
     year = {1994},
     volume = {20},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAM_1994_20_1_a9/}
}
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V. V. Kozlov. On tensor invariants of dynamical systems on three-dimensional manifolds. Theoretical and applied mechanics, Tome 20 (1994) no. 1, p. 119 . http://geodesic.mathdoc.fr/item/TAM_1994_20_1_a9/