| JIANG Qibao,HAN Mao'an.[J].数学年刊A辑,1999,20(2):233~246 |
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| MELNIKOV FUNCTIONS AND PERTURBATION OF A PLANARHAMILTONIAN SYSTEM |
| Received:January 16, 1997 Revised:October 23, 1998 |
| DOI： |
| 中文关键词: |
| 英文关键词:Melnikov functions, Bifurcation, Limit cycles |
| 基金项目: |
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| 中文摘要: |
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| 英文摘要: |
| In this paper, Melnikov functions which appear
in the study of limit cycles of a perturbed planar Hamiltonian 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 Melnikov functions and focal quantities (Theorem B).This relation is useful in both judging when a Melnikov function is identically zero and simplifying the computation of a Melnikov function
(see \S5).
Despite these results, this paper also includes other related results, e.g. some estimations of the upper bound for the number of limit cycles in a perturbed Hamiltonian system. |
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