Geodesic
Centering conditions for planar septic systems
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We find centering conditions for the following $$\displaylines{ \dot x=y+ x (H_2 (x,y)+H_6 (x,y)),\cr \dot y=-x+ y (H_2 (x,y)+H_6 (x,y)), }$$ where $H_2 (x,y)$ and $H_6 (x,y)$ are homogeneous polynomials of degrees 2 and 6, respectively. In some cases, we can find commuting systems and first integrals for the original system. We also study the geometry of the central region.
Classification : 34C05, 34C25
Keywords: centering conditions, isochronicity, commutativity 
@article{EJDE_2003__2003__a113,
     author = {Volokitin, Evgenii P.},
     title = {Centering conditions for planar septic systems},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a113/}
}
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Volokitin, Evgenii P. Centering conditions for planar septic systems. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a113/