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| Articolul precedent |
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 SM ISO690:2012PAŞCANU, Angela, SUBA, Alexandru. GL(2,R)-orbits of the polynomial sistems of differential equations. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2004, nr. 3(46), pp. 25-40. ISSN 1024-7696. |
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| Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | ||||||
| Numărul 3(46) / 2004 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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| Pag. 25-40 | ||||||
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| Rezumat | ||||||
In this work we study the orbits of the polynomial systems x˙ = P(x1, x2),
x˙ = Q(x1, x2) 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. |
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| Cuvinte-cheie Polynomial differential system, resonance, integrability., GL(2, R)-orbit |
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