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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2009, Number 2, Pages 29–54
(Mi basm225)
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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.
Received: 18.06.2009
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
Linking options:
https://www.mathnet.ru/eng/basm225 https://www.mathnet.ru/eng/basm/y2009/i2/p29
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