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 SM ISO690:2012SUBA, Alexandru, TURUTA (PODERIOGHIN), Silvia. Cubic differential systems with a weak focus and an affine real invariant straight line of maximal multiplicity. In: Conference on Applied and Industrial Mathematics: CAIM 2017, 14-17 septembrie 2017, Iași. Chișinău: Casa Editorial-Poligrafică „Bons Offices”, 2017, Ediţia 25, pp. 22-24. ISBN 978-9975-76-247-2. |
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| Conference on Applied and Industrial Mathematics Ediţia 25, 2017 |
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Conferința "Conference on Applied and Industrial Mathematics" Iași, Romania, 14-17 septembrie 2017 | ||||||
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| Pag. 22-24 | ||||||
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We consider the real cubic di erential system x_ = y + ax2 + cxy + fy2 + kx3 + mx2y + pxy2 + ry3 P(x; y); y_ = -(x + gx2 + dxy + by2 + sx3 + qx2y + nxy2 + ly3) Q(x; y); gcd(P;Q) = 1 (1) and the vector eld X = P (x; y) @ @x + Q(x; y) @ @y associated to the system (1). For the system (1) the origin of coordinates (0; 0) is a weak focus, i.e. is a singular point of focus or center type. An algebraic curve f(x; y) = 0; f 2 C[x; y] is called invariant algebraic curve of the system (1) if there exists a polynomial Kf 2 C[x; y] such that the identity X(f) f(x; y)Kf (x; y); (x; y) 2 R2 holds. |
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