Joyal, Pierre2019-03-192019-03-191998-10-09Joyal, P. (1998). Invariance of Poincare-Lyapunov polynomials under the group of rotations. <i>Electronic Journal of Differential Equations, 1998</i>(23), pp. 1-8.1072-6691https://hdl.handle.net/10877/7933We show that the Poincaré-Lyapunov polynomials at a focus of a family of real polynomial vector fields of degree n on the plane are invariant under the group of rotations. Furthermore, we show that under the multiplicative group ℂ* = {ρe iψ}, they are invariant up to a positive factor. These results follow from the weighted-homogeneity of the polynomials that we define in the text.Text8 pages1 file (.pdf)enAttribution 4.0 InternationalFocusInvariance of Poincare-Lyapunov polynomialsWeighted-homogeneityArticle