In this work an exhaustive numerical and analytical investigation of the dynamics of a bi-parametric symplectic map, the so-called rational standard map, at moderate-to-large values of the amplitude parameter is addressed. After reviewing the model, a discussion concerning an analytical determination of the maximum Lyapunov exponent is provided together with thorough numerical experiments. The theoretical results are obtained in the limit of a nearly uniform distribution of the phase values. Correlations among phases lead to departures from the expected estimates. In this direction, a detailed study of the role of stable periodic islands of periods 1, 2 and 4 is included. Finally, an experimental relationship between the Lyapunov and instability times is shown, while an analytical one applies when correlations are irrelevant, which is the case, in general, for large values of the amplitude parameter.

在这项工作中，对双参数辛映射（所谓的有理标准映射）的动力学进行了详尽的数值和分析研究，在振幅参数的中到大值下进行了处理。在回顾模型后，讨论了最大李雅普诺夫指数的分析确定以及全面的数值实验。理论结果是在相位值几乎均匀分布的极限下获得的。阶段之间的相关性导致偏离预期的估计。在这个方向上，详细研究了周期 1、周期 2 和周期 4 的稳定周期岛的作用。最后，显示了 Lyapunov 和不稳定时间之间的实验关系，而当相关性不相关时，分析关系适用，就是这种情况，