Geodesic
Dynamical systems that admit normal displacement
Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 3, pp. 386-395 Cet article a éte moissonné depuis la source Math-Net.Ru

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The classical geometrical construction of Bianchi–Lie, Bäcklund, and Darboux transformations is considered and generalized for dynamical systems. For a transformation that generalizes normal displacement, a class of dynamical systems that admit this transformation is found. A differential equation that distinguishes dynamical systems in $\mathbb R^2$ that belong to this class is derived, and some solutions of it are considered. 
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A. Yu. Boldin; R. A. Sharipov. Dynamical systems that admit normal displacement. Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 3, pp. 386-395. http://geodesic.mathdoc.fr/item/TMF_1993_97_3_a5/

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