Melnikov函数符号的应用

Applications of the Signs of Melnikov's Function

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.