关于三体问题的不稳定性与李雅普诺夫时间的关系
On the relationship between instability and Lyapunov times for the 3-body problem
摘要：
本文研究了三体系统的生存时间与李雅普诺夫时间之间的关系。结果表明，Sitnikov问题表现出两部分的幂律关系，如前所述的一般3体问题。使用一个近似的庞加莱映射在一个适当的表面上的部分，我们划定逃逸区域在一个域的初始条件，并使用这些区域解析地获得一个新的函数关系的李雅普诺夫时间和生存时间的三体问题。讨论了生存时间和李雅普诺夫时间的边际概率分布，证明了Sitnikov问题的李雅普诺夫时间的概率密度函数与一般三体问题的相似.
英文摘要：
In this study we consider the relationship between the survival time and the Lyapunov time for 3-body systems. It is shown that the Sitnikov problem exhibits a two-part power law relationship as demonstrated previously for the general 3-body problem. Using an approximate Poincare map on an appropriate surface of section, we delineate escape regions in a domain of initial conditions and use these regions to analytically obtain a new functional relationship between the Lyapunov time and the survival time for the 3-body problem. The marginal probability distributions of the Lyapunov and survival times are discussed and we show that the probability density function of Lyapunov times for the Sitnikov problem is similar to that for the general 3-body problem.
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