We present a numerical study of the application of the Shannon entropy technique to the planar restricted three-body problem in the vicinity of first-order interior mean-motion resonances with the perturber. We estimate the diffusion coefficient for a series of initial conditions and compare the results with calculations obtained from the time evolution of the variance in the semimajor-axis and eccentricity plane. Adopting adequate normalization factors, both methods yield comparable results, although much shorter integration times are required for entropy calculations. A second advantage of the use of entropy is that it is possible to obtain reliable results even without the use of ensembles or analysis restricted to surfaces of section or representative planes. This allows for a much more numerically efficient tool that may be incorporated into a working N-body code and applied to numerous dynamical problems in planetary dynamics. Finally, we estimate instability times for a series of initial conditions in the 2/1 and 3/2 mean-motion resonances and compare them with times of escape obtained from directed N-body simulations. We find very good agreement in all cases, not only with respect to average values but also in their dispersion for near-by trajectories

中文翻译：

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香农熵应用于平面受限三体问题

我们对香农熵技术在与扰动器的一阶内部平均运动共振附近的平面受限三体问题的应用进行了数值研究。我们估计了一系列初始条件的扩散系数，并将结果与​​从半长轴和偏心平面中方差的时间演变获得的计算进行比较。采用足够的归一化因子，两种方法都会产生可比较的结果，尽管熵计算需要更短的积分时间。使用熵的第二个优点是，即使不使用限于截面或代表性平面的表面的集成或分析，也可以获得可靠的结果。这允许在数值上更有效的工具，可以将其合并到有效的 N 体代码中，并应用于行星动力学中的众多动力学问题。最后，我们估计了 2/1 和 3/2 平均运动共振中一系列初始条件的不稳定时间，并将它们与从定向 N 体模拟获得的逃逸时间进行比较。我们在所有情况下都发现了非常好的一致性，不仅在平均值方面，而且在附近轨迹的离散性方面