In this work it is shown that the Shannon entropy is an efficient dynamical indicator that provides a direct measure of the diffusion rate and thus a time-scale for the instabilities arising when dealing with chaos. Its computation just involves the solution of the Hamiltonian flow, the variational equations are not required. After a review of the theory behind this approach, two particular applications are presented; a 4D symplectic map and the exoplanetary system HD 181433, approximated by the Planar Three Body Problem. Successful results are obtained for instability time-scales when compared with direct long range integrations (N-body or just iterations). Comparative dynamical maps reveal that this novel technique provides much more dynamical information than a classical chaos indicator.

在这项工作中，证明了香农熵是一种有效的动力学指标，它提供了扩散速率的直接量度，从而为处理混乱时产生的不稳定性提供了时间尺度。它的计算仅涉及哈密顿流的解，不需要变分方程。在回顾了这种方法背后的理论之后，提出了两个特殊的应用。一个4D辛映射图和系外行星系统HD 181433，由平面三体问题近似。与直接远距离积分（N体或仅迭代）相比，获得了不稳定性时标的成功结果。比较动态图显示，这种新技术比经典的混沌指标提供了更多的动态信息。