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Дифференциальные, интегральные и другие функциональные уравнения. Конечные разности. Вариационное исчисление. Функциональный анализ (246) |
SM ISO690:2012 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 | ||||||||
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CZU: 517.9 | ||||||||
MSC 2010: 34C05. | ||||||||
Pag. 13-40 | ||||||||
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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). |
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Cuvinte-cheie Cubic differential system, center problem, invariant straight line, algebraic multiplicity |
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