Subharmonic Solutions in Singular Systems
Subharmonic Solutions in Singular Systems
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DOI：
10.1006/jdeq.1996.0169
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发表时间：
1996-11
影响因子：
2.4
通讯作者：
F. Battelli;Michal Feckan
中科院分区：
文献类型：
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作者：
F. Battelli;Michal Feckan
摘要研究了一类周期奇异微分方程系统从同宿轨到周期轨的分支问题。我们使用泛函分析方法和Lyapunov-Schmidt方法得到了这个问题的分支函数，当e →0 +时，该分支函数趋向于著名的Melnikov函数。我们还研究了当周期轨道的周期趋于无穷大时分岔函数的行为。
Abstract We consider the problem of bifurcation from homoclinic towards periodic orbits for a periodic singular system of differential equations. We use a functional analytic approach and the Lyapunov–Schmidt method to obtain a bifurcation function for this problem which tends, as e →0 + , to the well-known Melnikov function for the bifurcation towards transverse homoclinic orbits. We also study the behavior of the bifurcation functions as the period of the periodic orbit tends to infinity.