Melnikov函数符号的应用*
Applications of the Signs of Melnikov’s Function
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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.
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关键词:
- Melnikov函数 /
- 流的余维二分支 /
- 分文集
Abstract: The existence and stability ol periodic solutions for the two-dimensional system x'=f(x)+εg(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. -
[1] Carr,J.,Applications of Center Manifold Theory,Springer-Verlag,New York (1981). [2] Draohman,B.,S.A.Van Gill and Zhang Zhi-fen,Abelian integrals for quadratic vector field,J.Reine Angew.math.,382(1987),165-180. [3] Gukenheimer,J.and P.Holmes.Nonlinear Oscillations,Dynamical Systems,and Bifurcations of Vector Field,Springer-Verlag,New York(1983). -
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