Abstract：The question on bifurcation of limit cycles in quadratic conservative perturbations of a quadratic integrable system is discussed. As a result of conservative perturbations, the first order Melnikov function for a perturbed system is identically equal to zero, so the second order Melnikov function has to be considered. The perturbation parameters which make no use in the first order Melnikov function may be important in the second order Melnikov function. Hence perturbed systems are more complicated. With the help of the formula for the second Melnikov function and theoretical analysis, the following result is obtained: if the first order Melnikov function for a perturbed system is identically equal to zero, and the second order Melnikov function for the perturbed system is not identically equal to zero, the system has at most two limit cycles.
彭临平. 一个二次可积系统在二次保守扰动下的分支[J]. 北京航空航天大学学报, 2000, 26(2): 235-238.
PENG Lin-ping. Bifurcation of a Quadratic Integrable System under Quadratic Conservative Perturbations. JOURNAL OF BEIJING UNIVERSITY OF AERONAUTICS AND A, 2000, 26(2): 235-238.
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