  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.
