Electronic Journal of Differential Equations,
Vol. 1998(1998), No. 23, pp. 1-8.

Title: Invariance of Poincare-Lyapunov polynomials under the group of rotations

Author: Pierre Joyal (Univ. du Quebec a Chicoutimi, Canada)

Abstract: 
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
${\Bbb C}^*=\{\rho {\rm e}^{i\psi}\}$, they are invariant up to a
positive factor. These results follow from the weighted-homogeneity
of the polynomials that we define in the text.


Submitted  June 25, 1998. Published October 9, 1998. 
Math Subject Classification: 58F14, 58F21, 58F35, 34C25.
Key Words: focus; invariance of Poincar\'e-Lyapunov polynomials; 
           weighted-homogeneity.