Geodesic
Centering conditions for planar septic systems
Electronic journal of differential equations, Tome 2003 (2003)
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__a13,
     author = {Volokitin,  Evgenii P.},
     title = {Centering conditions for planar septic systems},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1028.34033},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a13/}
}
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%A Volokitin,  Evgenii P.
%T Centering conditions for planar septic systems
%J Electronic journal of differential equations
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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__a13/