Geodesic
A class of integrable polynomial vector fields
Applicationes Mathematicae, Tome 23 (1996) no. 3, pp. 339-350.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We study the integrability of two-dimensional autonomous systems in the plane of the form $\dotx=-y+X_s(x,y)$, $\doty=x+Y_s(x,y)$, where X_s(x,y) and Y_s(x,y) are homogeneous polynomials of degree s with s≥2. First, we give a method for finding polynomial particular solutions and next we characterize a class of integrable systems which have a null divergence factor given by a quadratic polynomial in the variable $(x^2+y^2)^{s/2-1}$ with coefficients being functions of tan^{−1}(y/x).
DOI : 10.4064/am-23-3-339-350
Keywords: integrable systems in the plane, center-focus problem

Javier Chavarriga 1

1 
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Javier Chavarriga. A class of integrable polynomial vector fields. Applicationes Mathematicae, Tome 23 (1996) no. 3, pp. 339-350. doi : 10.4064/am-23-3-339-350. http://geodesic.mathdoc.fr/articles/10.4064/am-23-3-339-350/

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