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| MELNIKOV FUNCTIONS AND PERTURBATION OF A PLANARHAMILTONIAN SYSTEM |
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Citation： |
JIANG Qibao,HAN Mao'an.MELNIKOV FUNCTIONS AND PERTURBATION OF A PLANARHAMILTONIAN SYSTEM[J].Chinese Annals of Mathematics B,1999,20(2):233~246 |
| Page view： 1057
Net amount： 670 |
Authors： |
JIANG Qibao; HAN Mao'an |
Foundation： |
the National Natural Science
Foundation of China |
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| Abstract： |
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. |
Keywords： |
Melnikov functions, Bifurcation, Limit cycles |
Classification： |
34B02, 58F21, 58F14 |
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