| Abstract: | 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 inR
2 that belong to this class is derived, and some solutions of it are considered.State University, Bashkir. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 3, pp. 386–395, December, 1993. |
