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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
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