Geodesic
Metrizability of dynamical systems by a conformally equivalent metric
Teoretičeskaâ i matematičeskaâ fizika, Tome 103 (1995) no. 2, pp. 276-282
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For the Newtonian dynamical systems on Riemannian manifolds the problem of metrizability by means of conformally equivalent metric is solved. 
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R. A. Sharipov. Metrizability of dynamical systems by a conformally equivalent metric. Teoretičeskaâ i matematičeskaâ fizika, Tome 103 (1995) no. 2, pp. 276-282. http://geodesic.mathdoc.fr/item/TMF_1995_103_2_a7/

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