三体问题中的混沌与Lévy飞行
Chaos and Lévy Flights in the Three-Body Problem
摘要：
我们研究了一般引力三体问题中的混沌和Lévy飞行。我们引入了新的度量来表征时间演化和最终寿命分布，即扰频密度$\mathcal{S}$和LF指数$\mathcal{L}$，它们来自于Anosova映射和同源半径$R_{\mathcal{H}}$。基于这些指标，我们开发了详细的程序来隔离遍历相互作用和Lévy飞行相互作用。这使我们能够通过将三体寿命分布分解为不同类型相互作用的个体分布来更详细地研究三体寿命分布。我们观察到，各态历经的相互作用遵循类似于放射性衰变的指数衰变分布。同时，Lévy飞行相互作用遵循幂律分布。事实上，Lévy飞行在一般三体寿命分布的尾部占主导地位，为幂律尾部和Lévy飞行相互作用之间的推测联系提供了确凿的证据。我们提出了一个新的物理动机的三体系统的寿命分布模型，并讨论它如何可以用来提取有关的基本遍历和Lévy飞行相互作用的信息。我们讨论了质量弹射概率在三体系统中的遍历极限和比较以前的遍历形式主义。我们介绍了一种新的机制，一个三体松弛过程，并讨论其在一般的三体系统的相关性。
英文摘要：
We study chaos and Lévy flights in the general gravitational three-body problem. We introduce new metrics to characterize the time evolution and final lifetime distributions, namely Scramble Density $\mathcal{S}$ and the LF index $\mathcal{L}$, that are derived from the Agekyan-Anosova maps and homology radius $R_{\mathcal{H}}$. Based on these metrics, we develop detailed procedures to isolate the ergodic interactions and Lévy flight interactions. This enables us to study the three-body lifetime distribution in more detail by decomposing it into the individual distributions from the different kinds of interactions. We observe that ergodic interactions follow an exponential decay distribution similar to that of radioactive decay. Meanwhile, Lévy flight interactions follow a power-law distribution. Lévy flights in fact dominate the tail of the general three-body lifetime distribution, providing conclusive evidence for the speculated connection between power-law tails and Lévy flight interactions. We propose a new physically-motivated model for the lifetime distribution of three-body systems and discuss how it can be used to extract information about the underlying ergodic and Lévy flight interactions. We discuss mass ejection probabilities in three-body systems in the ergodic limit and compare it to previous ergodic formalisms. We introduce a novel mechanism for a three-body relaxation process and discuss its relevance in general three-body systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
