NEW STUDY ON THE CENTER PROBLEM AND BIFURCATIONS OF LIMIT CYCLES FOR THE LYAPUNOV SYSTEM (II)

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.