%0 Journal Article
%T Invariance of Poincare-Lyapunov polynomials under the group of rotations
%A Pierre Joyal
%J Electronic Journal of Differential Equations
%D 1998
%I Texas State University
%X We show that the Poincar'e-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 ${Bbb C}^*={ ho { m e}^{ipsi}}$, they are invariant up to a positive factor. These results follow from the weighted-homogeneity of the polynomials that we define in the text.
%K focus
%K invariance of Poincar'e-Lyapunov polynomials
%K weighted-homogeneity.
%U http://ejde.math.txstate.edu/Volumes/1998/23/abstr.html