MELNIKOV FUNCTIONS AND PERTURBATION OF A PLANAR
HAMILTONIAN SYSTEM |
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Authors: | JIANG Qibao and HAN Mao'an |
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Institution: | [1]DepartmentofAppliedMathematics,SoutheastUniversity,Nanjing210018,China [2]DepaxtmentofAppliedMathematics,ShanghaiJiaotongUaiver~ity~Shanghai200030,China |
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Abstract: | In this paper, Melnikov functions which apper in the study of limit cycles of a perturbed planar Hamiltonlan system are studied. There are two main contributions here. The first one is related to the explicit formulae for these functions: a new method is developed to achieve the goal for the second one (Theorem A). the authors also discover a close relation between Melnlkov functions and focal qtmntities (Theorem 13). This relation is useful in both judging when a Melnikov function is identically zero and simplifying the computation of a Melnikov function (see §5). I)espite these results, this paper also includes other related resuEs, e.g. some estimations of the upper bound for the number of limit cycles in a perturbed Hamiltonian system. |
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Keywords: | Melnikov functions Bifurcation Limit cycles |
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