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 827 3 |
| Ultima descărcare din IBN: 2023-09-23 11:35 |
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| 517.9 (248) |
| Ecuații diferențiale. Ecuații integrale. Alte ecuații funcționale. Diferențe finite. Calculul variațional. Analiză funcțională (246) |
 SM ISO690:2012SUBA, 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 |
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| 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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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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