Melnikov函数符号的应用  

Applications of the Signs of Melnikov's Function

作　　者：沈家骐 

机构地区：[1]上海师范大学

出　　处：《应用数学和力学》1992年第10期907-910,共4页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目

摘　　要：用Melnikov函数的符号判断未摄动系统是Hamilton系统的二维系统x′=f(x)+εg(x,a),0<ε<<1,a∈R的周期解的存在性和稳定性.其结果可应用于具有双重零特征值时流的余维二分支的分支集的相图构造.The existence and stability of periodic solutions for the two-dimensional system whose unperturbed system is 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 condimension two bifurcations of flows with double zero eigenvalues.

关 键 词：MELNIKOV函数 二维系统 周期解 

分 类 号：O175.1[理学—数学]