Displaying similar documents to “Congruence of analytic functions modulo a polynomial”

A class of integrable polynomial vector fields

Javier Chavarriga (1995)

Applicationes Mathematicae

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We study the integrability of two-dimensional autonomous systems in the plane of the form = - y + X s ( x , y ) , = x + Y s ( x , y ) , where Xs(x,y) and Ys(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).