Geodesic
Symmetry axes of planar polynomial differential systems
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 2, pp. 41-49 
V. B. Tlyachev; A. D. Ushkho; D. S. Ushkho. Symmetry axes of planar polynomial differential systems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 2, pp. 41-49. http://geodesic.mathdoc.fr/item/ISU_2010_10_2_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The notion of $N$-type axis of symmetry is introduced. It is proved that the vector field defined by system of the differential equations with $n$-order polynomials in a right hand, cannot have even number of axes of symmetry $N$-type at $n=2m$, $m\in N$. For $n=2,3$ full research of the given system on $N$-symmetry is carried out. Depending on the number of axes of $N$-type symmetry special forms of presenting of square and cubic systems,which allowto simplify qualitative research of such systems, are discovered.

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