%0 Journal Article
%T Centering conditions for planar septic systems
%A Evgenii P. Volokitin
%J Electronic Journal of Differential Equations
%D 2003
%I Texas State University
%X We find centering conditions for the following $O$-symmetric system of degree 7: $$displaylines{ dot x=y+ x (H_2 (x,y)+H_6 (x,y)),cr dot y=-x+ y (H_2 (x,y)+H_6 (x,y)), }$$ 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.
%K centering conditions
%K isochronicity
%K commutativity.
%U http://ejde.math.txstate.edu/Volumes/2003/34/abstr.html