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 SM ISO690:2012COZMA, Dumitru, SUBA, Alexandru. Partial integrals and the first focal value in the problem of centre. In: Nonlinear Differential Equations and Applications NoDEA, 1995, vol. 2, pp. 21-34. ISSN 1021-9722. DOI: https://doi.org/10.1007/BF01194012 |
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  Nonlinear Differential Equations and Applications NoDEA |
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| Volumul 2 / 1995 / ISSN 1021-9722 /ISSNe 1420-9004 | ||||||
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| DOI:https://doi.org/10.1007/BF01194012 | ||||||
| Pag. 21-34 | ||||||
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Polynomial differential systems of degree n≥3 on the plane are investigated. It is assumed that the origin O(0, 0) is a critical point with imaginary eigenvalues. We show that if the first focal value vanishes and there exist N=(n 2 +n-4)/2 partial algebraical integrals then the origin is a centre. For cubic systems (n=3), we have obtained fourteen series of conditions each ensuring that the origin is a centre. |
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| Cuvinte-cheie Center-focus problem, Cubic differential systems, integrability., invariant algebraic curves |
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