We show that the Poincare-Lyapunov polynomials at a focus of a family of real polynomial vector fields of degree on the plane are invariant under the group of rotations. Furthermore, we show that under the multiplicative group , 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 Poincare-Lyapunov polynomials, weighted-homogeneity.
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