三体问题中的Hamilton不变性和Lévy飞行
Hamiltonian intermittency and Lévy flights in the three-body problem
摘要：
我们考虑的中断和李雅普诺夫时间在一个层次的限制性三体问题的统计。我们表明，在破坏的边缘，逃逸体的轨道周期和轨道的大小表现出Lévy飞行。由于它们的存在，生存概率的时间衰减是重尾的，幂律指数等于-2/3，而李雅普诺夫函数与破坏时间之间的关系是拟线性的。这些结果的适用性在“分层共振散射”设置为三体相互作用进行了讨论。
英文摘要：
We consider statistics of the disruption and Lyapunov times in an hierarchical restricted three-body problem. We show that at the edge of disruption the orbital periods and the size of the orbit of the escaping body exhibit Lévy flights. Due to them, the time decay of the survival probability is heavy-tailed with the power-law index equal to -2/3, while the relation between the Lyapunov and disruption times is quasilinear. Applicability of these results in an "hierarchical resonant scattering" setting for a three-body interaction is discussed.
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