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IMI/Publicaţii/BASM/Ediţii/BASM n.3 (52), 2006/

Lie algebras of operators and invariant GL(2, ℜ)-integrals for Darboux type differential systems.

Authors: Diaconescu Oxana, Popa Mihail

Abstract

In this article two-dimensional autonomous Darboux type differential systems with nonlinearities of the ith degree with respect to the phase variables are considered. For every such system the admitted Lie algebra is constructed. With the aid of these algebras particular invariant GL(2, ℜ) -integrals as well as first integrals of considered systems are constructed. These integrals represent the algebraic curves of the (i-1)th degree. It is showed that the Darboux type systems with nonlinearities of the 2nd, the 4th and the 6th degree with respect to the phase variables do not have limit cycles.

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