This paper is concerned with the number and distribution of limit cycles of a perturbed quadratic Hamiltonian system which has 2 centers and 2 saddle points. The perturbation skills are applied to study the Hopf and heteroclinic bifurcation of such system under S2-reversible quartic perturbation. It is found that the perturbed system can have 6 limit cycles. The results acquired in this paper are useful to the study of the second part of 16th Hilbert Problem.
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