The problem of the center for cubic differential systems with the line at infinity and an affine real invariant straight line of total algebraic multiplicity five
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Дифференциальные, интегральные и другие функциональные уравнения. Конечные разности. Вариационное исчисление. Функциональный анализ (241)
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SUBA, Alexandru, TURUTA (PODERIOGHIN), Silvia. The problem of the center for cubic differential systems with the line at infinity and an affine real invariant straight line of total algebraic multiplicity five. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2019, nr. 2(90), pp. 13-40. 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

The problem of the center for cubic differential systems with the line at infinity and an affine real invariant straight line of total algebraic multiplicity five

CZU: 517.9
MSC 2010: 34C05.

Pag. 13-40

Suba Alexandru, Turuta (Poderioghin) Silvia
 
Vladimir Andrunachievici Institute of Mathematics and Computer Science
 
Disponibil în IBN: 3 ianuarie 2020


Rezumat

In this article, we study the real planar cubic differential systems with a non-degenerate monodromic critical point M0. In the cases when the algebraic multiplicity m(Z) = 5 or m(l1) + m(Z) ≥ 5, where Z = 0 is the line at infinity and l1 = 0 is an affine real invariant straight line, we prove that the critical point M0 is of the center type if and only if the first Lyapunov quantity vanishes. More over, if m(Z) = 5 (respectively, m(l1) +m(Z) ≥ 5, m(l1) ≥ j, j = 2, 3) then M0 is a center if the cubic systems have a polynomial first integral (respectively, an integrating factor of the form 1/lj 1).

Cuvinte-cheie
Cubic differential system, center problem, invariant straight line, algebraic multiplicity

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