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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2017, Number 2, Pages 112–130
(Mi basm450)
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This article is cited in 1 scientific paper (total in 1 paper)
Research articles
The Lyapunov quantities and the center conditions for a class of bidimensional polynomial systems of differential equations with nonlinearities of the fourth degree
Iurie Calina, Stanislav Ciubotarub a Institute of Mathematics and Computer Science
Academy of Sciences of Moldova, Chişinău, Moldova
b Moldova State University, Chişinău, Moldova
Abstract:
For the autonomous bidimensional polynomial systems of differential equations with nonlinearities of the fourth degree the $GL(2,\mathbb R)$-invariant recurrence equations for determination of the Lyapunov quantities were established. Moreover, the general form of Lyapunov quantities for the mentioned systems is obtained. For a class of such systems the necessary and sufficient $GL(2,\mathbb R)$-invariant conditions for the existence of center are given.
Keywords and phrases:
polynomial differential systems, invariant, comitant, transvectant, Lyapunov quantities, center conditions.
Received: 07.11.2016
Citation:
Iurie Calin, Stanislav Ciubotaru, “The Lyapunov quantities and the center conditions for a class of bidimensional polynomial systems of differential equations with nonlinearities of the fourth degree”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 2, 112–130
Linking options:
https://www.mathnet.ru/eng/basm450 https://www.mathnet.ru/eng/basm/y2017/i2/p112
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Abstract page: | 258 | Full-text PDF : | 58 | References: | 25 |
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