Geodesic
Invariance of Poincaré-Lyapunov polynomials under the group of rotations
Electronic journal of differential equations, Tome 1998 (1998)
We show that the Poincare-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.
Classification : 58F14, 58F21, 58F35, 34C25
Keywords: focus, invariance of Poincarè-Lyapunov polynomials, weighted-homogeneity 
@article{EJDE_1998__1998__a4,
     author = {Joyal,  Pierre},
     title = {Invariance of {Poincar\'e-Lyapunov} polynomials under the group of rotations},
     journal = {Electronic journal of differential equations},
     year = {1998},
     volume = {1998},
     zbl = {0924.58089},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a4/}
}
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JO  - Electronic journal of differential equations
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%0 Journal Article
%A Joyal,  Pierre
%T Invariance of Poincaré-Lyapunov polynomials under the group of rotations
%J Electronic journal of differential equations
%D 1998
%V 1998
%U http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a4/
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%F EJDE_1998__1998__a4
Joyal,  Pierre. Invariance of Poincaré-Lyapunov polynomials under the group of rotations. Electronic journal of differential equations, Tome 1998 (1998). http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a4/