The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials
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Mathematics (1245)
Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis (171)
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SCHLOMIUK, Dana; VULPE, Nicolae. The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials. In: Buletinul Academiei de Ştiinţe a Moldovei. Matematica. 2019, nr. 2(90), pp. 41-55. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Moldovei. Matematica
Numărul 2(90) / 2019 / ISSN 1024-7696

The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials

CZU: 515+517.9
MSC 2010: 58K45, 34C05, 34C23, 34A34.

Pag. 41-55

Schlomiuk Dana1, Vulpe Nicolae2
 
1 Université de Montréal,
2 Vladimir Andrunachievici Institute of Mathematics and Computer Science
 
Disponibil în IBN: 3 ianuarie 2020


Rezumat

In this paper we provide affine invariant necessary and sufficient conditions for a non-degenerate quadratic differential system to have an invariant conic f(x, y) = 0 and a Darboux invariant of the form f(x, y)est with , s ∈ R and s 6= 0. The family of all such systems has a total of seven topologically distinct phase portraits. For each one of these seven phase portraits we provide necessary and sufficient conditions in terms of affine invariant polynomials for a non-degenerate quadratic system in this family to possess this phase portrait.

Cuvinte-cheie
quadratic differential system, invariant conic, Darboux invariant, affine invariant polynomial, Group action, phase portrait

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<dc:creator>Schlomiuk, D.</dc:creator>
<dc:creator>Vulpe, N.I.</dc:creator>
<dc:date>2019-12-27</dc:date>
<dc:description xml:lang='en'><p>In this paper we provide affine invariant necessary and sufficient conditions for a non-degenerate quadratic differential system to have an invariant conic f(x, y) = 0 and a Darboux invariant of the form f(x, y)est with , s &isin; R and s 6= 0. The family of all such systems has a total of seven topologically distinct phase portraits. For each one of these seven phase portraits we provide necessary and sufficient conditions in terms of affine invariant polynomials for a non-degenerate quadratic system in this family to possess this phase portrait.</p></dc:description>
<dc:source>Buletinul Academiei de Ştiinţe a Moldovei. Matematica 90 (2) 41-55</dc:source>
<dc:subject>quadratic differential system</dc:subject>
<dc:subject>invariant conic</dc:subject>
<dc:subject>Darboux
invariant</dc:subject>
<dc:subject>affine invariant polynomial</dc:subject>
<dc:subject>Group action</dc:subject>
<dc:subject>phase portrait</dc:subject>
<dc:title><p>The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials</p></dc:title>
<dc:type>info:eu-repo/semantics/article</dc:type>
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