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 SM ISO690:2012DIACONESCU, Oxana, POPA, Mihail. Lie algebras of operators and invariant
GL(2,R)-integrals for Darboux type differential systems. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2006, nr. 3(52), pp. 3-16. ISSN 1024-7696. |
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| Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | ||||||
| Numărul 3(52) / 2006 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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| Pag. 3-16 | ||||||
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In this article two-dimensional autonomous Darboux type differential systems with nonlinearities of the ith (i = 2, 7) 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 (i = 2, 7) 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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| Cuvinte-cheie The Darboux type differential system, invariant GL(2, R)-integrating factor, invariant GL(2, R)-integral, limit cycle., comitant |
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