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 SM ISO690:2012SUBA, Alexandru, VACARAŞ, Olga. Cubic differential systems with an invariant straight line of maximal multiplicity. In: Annals of the University of Craiova, Mathematics and Computer Science Series, 2015, vol. 42, nr. 2, pp. 427-449. ISSN 1223-6934. |
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  Annals of the University of Craiova, Mathematics and Computer Science Series |
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| Volumul 42, Numărul 2 / 2015 / ISSN 1223-6934 | ||||||
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| Pag. 427-449 | ||||||
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In this work the estimation 3n-2 ≤Ma(n) ≤ 3n -1 of maximal algebraic multiplicity Ma(n) of an invariant straight line is obtained for two-dimensional polynomial diffierential systems of degree n ≥2. In the class of cubic systems (n = 3) we have Ma(3) = 7: Moreover, we prove that if an affine real invariant straight line has multiplicity equal to 1 (respectively, 2,3,4,5,6,7), then the maximal multiplicity of the line at innity is 7 (respectively, 5,5,5,4,1,1). Each of these cubic systems has a single affine invariant straight line, is Darboux integrable and their normal forms are given. |
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| Cuvinte-cheie Algebraic (geometric) multiplicity, Cubic differential system, invariant straight line |
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