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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2019, номер 2, страницы 13–40
(Mi basm505)
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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
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
Alexandru Şubăa, Silvia Turutab a Vladimir Andrunachievici Institute of Mathematics
and Computer Science,
5 Academiei str., Chişinău, MD 2028, Moldova
b Tiraspol State University,
5 Gh. Iablocichin str., Chişinău, MD-2069, Moldova
Аннотация:
In this article, we study the real planar cubic differential systems with a non-degenerate monodromic critical point $M_0.$ In the cases when the algebraic multiplicity $m(Z)= 5$ or $m(l_1)+m(Z)\ge 5,$ where $Z=0$ is the line at infinity and $l_1=0$ is an affine real invariant straight line, we prove that the critical point $M_0$ is of the center type if and only if the first Lyapunov quantity vanishes. More over, if $m(Z)=5$ (respectively, $m(l_1)+m(Z)\ge 5,~ m(l_1)\ge j,~ j=2,3 $) then $M_0$ is a center if the cubic systems have a polynomial first integral (respectively, an integrating factor of the form $1/l_1^j$).
Ключевые слова и фразы:
cubic differential system, center problem, invariant straight line, algebraic multiplicity.
Поступила в редакцию: 18.03.2019
Образец цитирования:
Alexandru Şubă, Silvia Turuta, “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”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2019, no. 2, 13–40
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/basm505 https://www.mathnet.ru/rus/basm/y2019/i2/p13
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Страница аннотации: | 256 | PDF полного текста: | 90 | Список литературы: | 36 |
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