﻿﻿ ﻿ ﻿﻿ 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
 Conţinutul numărului revistei Articolul precedent Articolul urmator 799 3 Ultima descărcare din IBN: 2023-09-23 11:35 Căutarea după subiecte similare conform CZU 517.9 (248) Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis (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. EXPORT metadate: Google Scholar Crossref CERIF DataCiteDublin Core
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

 Autori: 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

### Dublin Core Export

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<dc:creator>Şubă, A.S.</dc:creator>
<dc:creator>Turuta (Poderioghin), S.I.</dc:creator>
<dc:date>2019-12-27</dc:date>
<dc:description xml:lang='en'><p>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) &ge; 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) &ge; 5, m(l1) &ge; 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).</p></dc:description>
<dc:source>Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica 90 (2) 13-40</dc:source>
<dc:subject>Cubic differential system</dc:subject>
<dc:subject>center problem</dc:subject>
<dc:subject>invariant
straight line</dc:subject>
<dc:subject>algebraic multiplicity</dc:subject>
<dc:title>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</dc:title>
<dc:type>info:eu-repo/semantics/article</dc:type>
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