Volokitin, Evgenii P.2020-10-052020-10-052003-04-03Volokitin, E. P. (2003). Centering conditions for planar septic systems. <i>Electronic Journal of Differential Equations, 2003</i>(34), pp. 1-7.1072-6691https://hdl.handle.net/10877/12706We find centering conditions for the following O-symmetric system of degree 7: ẋ = y + x(H2(x, y) + H6(x, y)), ẏ = -x + y(H2(x, y) + H6(x, y)), where H2(x, y) and H6(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.Text7 pages1 file (.pdf)enAttribution 4.0 InternationalCentering conditionsIsochronicityCommutativityArticle