Geodesic
Some tensor invariants of geodesic, potential, and dissipative systems on the tangent bundles of three-dimensional manifolds
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 210 (2022), pp. 96-105

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In this paper, we present tensor invariants (differential forms) for homogeneous dynamical systems on the tangent bundles of smooth three-dimensional manifolds and demonstrate the connection between the presence of these invariants and the existence of a complete set of first integrals, which is necessary for integrating geodesic, potential, and dissipative systems.
Keywords: dynamical system, integrability, dissipation, transcendental first integral, invariant differential form. 
@article{INTO_2022_210_a9,
     author = {M. V. Shamolin},
     title = {Some tensor invariants of geodesic, potential, and dissipative systems on the tangent bundles of three-dimensional manifolds},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {96--105},
     publisher = {mathdoc},
     volume = {210},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_210_a9/}
}
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M. V. Shamolin. Some tensor invariants of geodesic, potential, and dissipative systems on the tangent bundles of three-dimensional manifolds. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 210 (2022), pp. 96-105. http://geodesic.mathdoc.fr/item/INTO_2022_210_a9/