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Limit cycles of polynomial vector fields with nondegenerate singular points on the real plane. (Russian) Zbl 0549.34033
The author has shown earlier that the proof of the well-known theorem of Dulac on the finiteness of the number of limit cycles of a polynomial vector field on the plane was not complete. In this paper the following main theorem is established. Assume that every singular point (finite or in the infinity) of a polynomial vector field on the plane is nondegenerate. Then the number of limit cycles is finite.
Reviewer: S.Yu.Pilyugin

MSC:
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
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