New sufficient conditions for a center and global phase portraits for polynomial systems.

Título inglés New sufficient conditions for a center and global phase portraits for polynomial systems.
Título español Nuevas condiciones suficientes para retratos de fase centrales y globales para sistemas polinómicos.
Autor/es Giacomini, Hector ; Ndiaye, Malick
Organización Lab. Modèl. Phys. Math. Fac. Sci. Techn. Univ. Tours, Tours, Francia
Revista 0214-1493
Publicación 1996, 40 (2): 351-372, 19 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés In this paper we consider cubic polynomial systems of the form: x' = y + P(x, y), y' = −x + Q(x, y), where P and Q are polynomials of degree 3 without linear part. If M(x, y) is an integrating factor of the system, we propose its reciprocal V (x, y) = 1 / M(x,y) as a linear function of certain coefficients of the system. We find in this way several new sets of sufficient conditions for a center. The resulting integrating factors are of Darboux type and the first integrals are in the Liouville form.
By induction, we have generalized these results for polynomial systems of arbitrary degree.
Moreover, for the cubic case, we have constructed all the phase portraits for each new family with a center.
Clasificación UNESCO 121013 ; 120602 ; 120219
Palabras clave español Modelo dinámico ; Ecuaciones polinómicas ; Ecuaciones diferenciales ; Resolución de ecuaciones ; Integrabilidad ; Ecuación de Liouville
Código MathReviews MR1425623
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