Sufficient GL(2,R)-invariant center conditions for some classes of two-dimensional cubic differential systems

Calin Iurie; Baltag Valeriu

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695

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2020-01-09 15:33

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517.9 (254)

Ecuații diferențiale. Ecuații integrale. Alte ecuații funcționale. Diferențe finite. Calculul variațional. Analiză funcțională (252)

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CALIN, Iurie, BALTAG, Valeriu. Sufficient GL(2,R)-invariant center conditions for some classes of two-dimensional cubic differential systems. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2019, nr. 2(90), pp. 127-136. ISSN 1024-7696.

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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica

Numărul 2(90) / 2019 / ISSN 1024-7696 /ISSNe 2587-4322

Sufficient GL(2,R)-invariant center conditions for some classes of two-dimensional cubic differential systems

CZU: 517.9

MSC 2010: 34C05, 58F14.

Pag. 127-136

Calin Iurie, Baltag Valeriu

Vladimir Andrunachievici Institute of Mathematics and Computer Science

Disponibil în IBN: 4 ianuarie 2020

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Rezumat

The autonomous two-dimensional polynomial cubic systems of differential equations with pure imaginary eigenvalues of the Jacobian matrix at the singular point (0, 0) are considered in this paper. The center problem was studied for three classes of such systems: the class of cubic systems with zero divergence of the cubic homogeneities (S3 ≡ 0), the class of cubic systems with zero divergence of the quadratic homogeneities (S2 ≡ 0) and the class of cubic systems with nonzero divergence of the quadratic homogeneities (S2 6≡ 0). For these systems, sufficient GL(2,R)-invariant center conditions for the origin of coordinates of the phase plane were established.

Cuvinte-cheie
Polynomial differential systems, invariant, comitant, transvectant, center conditions, linear transformation, rotation transformation, symmetry axis

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