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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2006, Number 3, Pages 3–16 (Mi basm104)  

This article is cited in 2 scientific papers (total in 2 papers)

Lie algebras of operators and invariant $GL(2,\mathbb{R})$-integrals for Darboux type differential systems

O. V. Diaconescu, M. N. Popa

Institute of Mathematics and Computer Sciences, Academy of Sciences of Moldova, Chisinau, Moldova

Abstract: In this article two-dimensional autonomous Darboux type differential systems with nonlinearities of the $i^{th} (i=\overline{2,7})$ 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 $GL(2,\mathbb{R})$-integrals as well as first integrals of considered systems are constructed. These integrals represent the algebraic curves of the $(i-1)^{th}(i=\overline{2,7})$ degree. It is showed that the Darboux type systems with nonlinearities of the $2^{nd}$, the $4^{th}$ and the $6^{th}$ degree with respect to the phase variables do not have limit cycles.

Keywords and phrases: Darboux type differential system, comitant, invariant $GL(2,\mathbb{R})$-integrating factor, invariant $GL(2,\mathbb{R})$-integral, limit cycle.

Full text: PDF file (162 kB)
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Bibliographic databases:

MSC: 34C05, 34C14
Received: 21.08.2006
Language: English

Citation: O. V. Diaconescu, M. N. Popa, “Lie algebras of operators and invariant $GL(2,\mathbb{R})$-integrals for Darboux type differential systems”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2006, no. 3, 3–16

Citation in format AMSBIB
\Bibitem{DiaPop06}
\by O.~V.~Diaconescu, M.~N.~Popa
\paper Lie algebras of operators and invariant $GL(2,\mathbb{R})$-integrals for Darboux type differential systems
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2006
\issue 3
\pages 3--16
\mathnet{http://mi.mathnet.ru/basm104}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2300505}
\zmath{https://zbmath.org/?q=an:1129.34028}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. V. Diaconescu, “Multi-dimensional Darboux type differential systems with quadratic nonlinearities”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2007, no. 1, 95–100  mathnet  mathscinet  zmath
    2. V. Baltag, I. Calin, “The transvectants and the integrals for Darboux systems of differential equations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2008, no. 1, 4–18  mathnet  mathscinet  zmath
  • Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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