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
Закрыть
Conţinutul numărului revistei
Articolul precedent
Articolul urmator
248 2
Ultima descărcare din IBN:
2020-06-13 15:56
Căutarea după subiecte
similare conform CZU
517.9 (152)
Дифференциальные, интегральные и другие функциональные уравнения. Конечные разности. Вариационное исчисление. Функциональный анализ (151)
SM ISO690:2012
ŞUBĂ, 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 Moldovei. Matematica. 2019, nr. 2(90), pp. 13-40. ISSN 1024-7696.
EXPORT metadate:
Google Scholar
Crossref
CERIF

DataCite
Dublin Core
Buletinul Academiei de Ştiinţe a Moldovei. Matematica
Numărul 2(90) / 2019 / ISSN 1024-7696

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

Şubă Alexandru, Turuta (Poderioghin) Silvia
 
Vladimir Andrunakievich 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