Scattering of trajectories at a separatrix under autoresonance
Scattering of trajectories at a separatrix under autoresonance
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DOI：
10.1063/1.4875105
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发表时间：
2014-06
影响因子：
1.3
通讯作者：
O. Kiselev;N. Tarkhanov
中科院分区：
文献类型：
--
作者：
O. Kiselev;N. Tarkhanov
本文的题目是一个自共振方程的解。我们寻找有界为t →−∞的解的参数与两个双参数解族的参数之间的联系。一个族由未被捕获到共振的解组成，另一个族由被捕获到共振的那些递增解组成。用这种方法描述了参数缓变方程通过分界线的过渡，并得到了这些解在共振前的参数估计，这些解可能被捕获到自共振中。
The subject of this paper is solutions of an autoresonance equation. We look for a connection between the parameters of the solution bounded as t →−∞, and the parameters of two two-parameter families of solutions as t → ∞. One family consists of the solutions which are not captured into resonance, and another of those increasing solutions which are captured into resonance. In this way we describe the transition through the separatrix for equations with slowly varying parameters and get an estimate for parameters before the resonance of those solutions which may be captured into autoresonance.