In this paper, Melnikov functions which appear in the study of limit cycles of a perturbedplanar Hamiltonian system are studied. There are two main contributions here. The first oneis related to the explicit formulae ...In this paper, Melnikov functions which appear in the study of limit cycles of a perturbedplanar Hamiltonian system are studied. There are two main contributions here. The first oneis related to the explicit formulae for these functions: a new method is developed to achievethe goal for the second one (Theorem A). the authors also discover a close relation betweenMelnikov functions and focal quantities (Theorem B). This relation is useful in both judgingwhen a Melnikov function is identically zero and simplifying the computation of a Melnikovfunction (see 5). Despite these results, this paper also includes other related results, e.g. someestimations of the upper bound for the number of limit cycles in a perturbed Hamiltoniansystem.展开更多
文摘In this paper, Melnikov functions which appear in the study of limit cycles of a perturbedplanar Hamiltonian system are studied. There are two main contributions here. The first oneis related to the explicit formulae for these functions: a new method is developed to achievethe goal for the second one (Theorem A). the authors also discover a close relation betweenMelnikov functions and focal quantities (Theorem B). This relation is useful in both judgingwhen a Melnikov function is identically zero and simplifying the computation of a Melnikovfunction (see 5). Despite these results, this paper also includes other related results, e.g. someestimations of the upper bound for the number of limit cycles in a perturbed Hamiltoniansystem.
