Song, Yan The Poincaré bifurcation of cubic non-Hamiltonian integrable systems with double centers. (Chinese. English summary) Zbl 1174.34394 Chin. J. Eng. Math. 25, No. 4, 679-684 (2008). Summary: We study the Poincaré bifurcation of cubic non-Hamiltonian integrable systems with double centers. The proof relies on an estimation of the number of zeros of a related Abelian integrals. We show that the Poincaré bifurcation can generate six limit cycles after a small cubic perturbation. MSC: 34C23 Bifurcation theory for ordinary differential equations 34C08 Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 37G10 Bifurcations of singular points in dynamical systems Keywords:cubic non-Hamiltonian integrable system; Poincaré bifurcation; Picard-Fuchs equation; limit cycle; Abelian integral PDFBibTeX XMLCite \textit{Y. Song}, Chin. J. Eng. Math. 25, No. 4, 679--684 (2008; Zbl 1174.34394)