The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials
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515+517.9 (1)
Matematică (1144)
Ecuații diferențiale. Ecuații integrale. Alte ecuații funcționale. Diferențe finite. Calculul variațional. Analiză funcțională (155)
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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 Andrunakievich 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