A class of integrable polynomial vector fields

Volume 23 / 1995

Javier Chavarriga Applicationes Mathematicae 23 (1995), 339-350 DOI: 10.4064/am-23-3-339-350


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).


  • Javier Chavarriga

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