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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2004, Number 3, Pages 25–40
(Mi basm176)
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This article is cited in 2 scientific papers (total in 2 papers)
Research articles
$GL(2,R)$-orbits of the polynomial sistems of differential equations
Angela Păşcanua, Alexandru Şubăb a Department of Mathematics, State University of Tiraspol, Chişinău, Moldova
b Department of Mathematics, State University of Moldova, Chişinău, Moldova
Abstract:
In this work we study the orbits of the polynomial systems $\dot x=P(x_1,x_2)$, $\dot x=Q(x_1,x_2)$ by the action of the group of linear transformations $GL(2,R)$. It is shown that there are not polynomial systems with the dimension of $GL$-orbits equal to one and there exist $GL$-orbits of the dimension zero only for linear systems. On the basis of the dimension of $GL$-orbits the classification of polynomial systems with a singular point $O(0,0)$ with real and distinct eigenvalues is obtained. It is proved that on $GL$-orbits of the dimension less than four these systems are Darboux integrable.
Keywords and phrases:
Polynomial differential system, $GL(2,R)$-orbit, resonance, integrability.
Received: 02.11.2004
Citation:
Angela Păşcanu, Alexandru Şubă, “$GL(2,R)$-orbits of the polynomial sistems of differential equations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2004, no. 3, 25–40
Linking options:
https://www.mathnet.ru/eng/basm176 https://www.mathnet.ru/eng/basm/y2004/i3/p25
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Abstract page: | 247 | Full-text PDF : | 51 | References: | 45 | First page: | 1 |
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