On the continuability of solutions of autonomous differential systems

V. V. Amel'kin^a, V. Yu. Tyshchenko<sup>b

a</sup> Belorussian State University, 4 Nezavisimosti Ave., Minsk, 220030 Republic of Belarus
^b Grodno State University, 4 Oszeshko str., Grodno, 230023 Republic of Belarus

Abstract: Problems about a continuability of solutions of real autonomous systems of equations in total differentials and about a reducibility of such systems to many-dimensional dynamical systems are investigated. The reducibility criterion is proved. Conditions at which realisation the reducible system of exact differential equations has orbits–torus-cylinders, are received. Examples are given. When the received outcomes can be transferred on a complex case is noted.

Keywords: autonomous system, quite solvable system of the exact equations, continuability of the solutions, many-dimensional dynamical system, orbit.

UDC: 517.925

Received: 19.12.2019
Revised: 19.12.2019
Accepted: 25.03.2020

DOI: 10.26907/0021-3446-2020-11-15-28

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:11, 11–22

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