Laboratory of Information Technologies

Date and Time: Thursday, 29 September 2022, at 3:00 PM

Venue: room 310, Laboratory of Information Technologies; online seminar via Zoom

Information about seminar and link to join

Seminar topic: “On the trajectories of dynamical systems lying on algebraic hypersurfaces”

Speaker: Mikhail Malykh

Authors: E. A. Ayryan¹, M. M. Gambaryan², M. D. Malykh^{1, 2}, L. A. Sevastianov<sup>1, 2

1</sup> – JINR
² – RUDN

Abstract:

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 generalisation 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.