Труды Института механики им. Р.Р. Мавлютова

ISSN 2542–0380

Электронный научный журнал | Electronic Scientific Journal

Proceedings of the Mavlyutov Institute of Mechanics

Zhiber A.V., Kostrigina O.S. Integrable two-dimensional dynamical systems and the characteristic Lie algebras Proceedings of the Institute of Mechanics of Ufa Branch of RAS. 5 (2007). 195–200.

2007. Vol. 5. Issue 1, Pp. 195–200
URL: http://proc.uimech.org/uim2007.1.023,en
DOI: 10.21662/uim2007.1.023

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

Zhiber A.V., Kostrigina O.S.

Institute of Mathematics, Ufa
Ufa State Aviation Technical University, Ufa

Abstract

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

Keywords

integrals,
characteristic Lie algebra,
Laplace invariants