Geodesic
Dynamical systems that admit normal displacement
Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 3, pp. 386-395

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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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     author = {A. Yu. Boldin and R. A. Sharipov},
     title = {Dynamical systems that admit normal displacement},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {386--395},
     publisher = {mathdoc},
     volume = {97},
     number = {3},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_97_3_a5/}
}
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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/