Thursday, September 29, 2022
Room 310, Online seminar via Zoom
Ayryan E.A. (1), Gambaryan M.M. (2), Malykh M.D. (1,2), Sevastianov L.A. (1,2)
1 - JINR, 2 - RUDN

On the trajectories of dynamical systems lying on algebraic hypersurfaces

The following problem is considered: a dynamic system and a linear system of algebraic hypersurfaces are given, it is necessary to find out whether the trajectories of the dynamic system lie on hypersurfaces of the linear system. Using the theory of Lagutinski determinants, we present the solution to this problem. It is shown that in the case of the affirmative answer, the dynamic system has an algebraic integral of motion, but at the same time the hypersurfaces of the linear system themselves do not have to be integral. A generalization for the case of approximate trajectories of dynamic systems, calculated according to reversible difference schemes, is given. The connection between Lagutinski's determinants and their difference analogues was discussed.

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