APPLICATIONS OF THE SIGNS OF MELNIKOV'S FUNCTION  

作　　者：沈家骐 

机构地区：[1]Shanghai Normal University, Shanghai

出　　处：《Applied Mathematics and Mechanics(English Edition)》1992年第10期947-950,共4页应用数学和力学（英文版）

基　　金：The project is supported by the National Natural Science Foundation of China

摘　　要：The existence and stability ol periodic solutions for the two-dimensional system x' = f(x)+?g(x ,a), 0<ε<<1 ,a?R whose unperturbed systemis Hamiltonian can be decided by using the signs of Melnikov's function. The results can be applied to the construction of phase portraits in the bifurcation set of codimension two bifurcations of flows with doublezero eigenvalues.The existence and stability ol periodic solutions for the two-dimensional system x' = f(x)+?g(x ,a), 0<ε<<1 ,a?R whose unperturbed systemis Hamiltonian can be decided by using the signs of Melnikov's function. The results can be applied to the construction of phase portraits in the bifurcation set of codimension two bifurcations of flows with doublezero eigenvalues.

关 键 词：Melnikov's function codimension two bifurcations of flows bifurcation set 

分 类 号：O3，O1[理学—力学]