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New study on the center problem and bifurcations of limit cycles for the Lyapunov system. II. (English) Zbl 1179.34030
Summary: The center problem and bifurcations of limit cycles for the Lyapunov system are continuously studied. We shall prove that we can construct successively a formal series such that the Lyapunov system is reduced a half-normal form. From the coefficients of the half-normal form, we obtain directly the Lyapunov constants of the origin. As examples, for two classes of cubic systems, the center and focus problem, and multiple bifurcations of limit cycles are studied.

MSC:
 34C05 Location of integral curves, singular points, limit cycles (ODE) 34C25 Periodic solutions of ODE 34C20 Transformation and reduction of ODE and systems, normal forms 34C23 Bifurcation (ODE)
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