Il’yashenko, Yu. S. Limit cycles of polynomial vector fields with nondegenerate singular points on the real plane. (Russian) Zbl 0549.34033 Funkts. Anal. Prilozh. 18, No. 3, 32-42 (1984). 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 Cited in 2 ReviewsCited in 5 Documents 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 Keywords:limit cycles; singular point PDFBibTeX XMLCite \textit{Yu. S. Il'yashenko}, Funkts. Anal. Prilozh. 18, No. 3, 32--42 (1984; Zbl 0549.34033)