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The Poincaré bifurcation of cubic non-Hamiltonian integrable systems with double centers. (Chinese. English summary) Zbl 1174.34394

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
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