# zbMATH — the first resource for mathematics

Complete qualitative study of a cubic differential system. (Russian) Zbl 0825.34019
A differential system with cubic right-hand sides is studied in the Poincaré circle. The system has an algebraic integral of the form $$F_ 1^ 2F_ 2^{-3}=C$$, where $$F_ 1(x,y)$$ and $$F_ 2(x,y)$$ are respectively the sixth and fourth order polynomials with real coefficients. There exists a complex singular point on the Poincaré circle, which coincides with the ”ends” of the $$0y$$-axis.
##### MSC:
 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
Full Text: