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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2009, Number 2, Pages 29–54 (Mi basm225)  

This article is cited in 1 scientific paper (total in 1 paper)

Research articles

A complete classification of quadratic differential systems according to the dimensions of $Aff(2,\mathbb R)$-orbits

N. Gherstega, V. Orlov, N. Vulpe

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

Abstract: In this article we consider the action of the group $Aff(2,\mathbb R)$ of affine transformations and time rescaling on real planar quadratic differential systems. Via affine invariant conditions we give a complete stratification of this family of systems according to the dimension $\mathcal D$ of affine orbits proving that $3\le\mathcal D\le6$. Moreover we give a complete topological classification of all the systems located on the orbits of dimension $\mathcal D\le5$ constructing the affine invariant criteria for the realization of each of 49 possible topologically distinct phase portraits.

Keywords and phrases: quadratic differential system, Lie algebra of operators, $Aff(2,\mathbb R)$-orbit, affine invariant polynomial.

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Document Type: Article
MSC: 34C14
Received: 18.06.2009
Language: English

Citation: N. Gherstega, V. Orlov, N. Vulpe, “A complete classification of quadratic differential systems according to the dimensions of $Aff(2,\mathbb R)$-orbits”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2009, no. 2, 29–54

Citation in format AMSBIB
\Bibitem{GheOrlVul09}
\by N.~Gherstega, V.~Orlov, N.~Vulpe
\paper A complete classification of quadratic differential systems according to the dimensions of $Aff(2,\mathbb R)$-orbits
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2009
\issue 2
\pages 29--54
\mathnet{http://mi.mathnet.ru/basm225}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2589927}
\zmath{https://zbmath.org/?q=an:1202.34070}


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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. Dana Schlomiuk, “New developments based on the mathematical legacy of C. S. Sibirschi”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2013, no. 1, 3–10  mathnet  mathscinet
  • Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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