The mean Poincaré recurrence time as well as the Lyapunov time are measured for the Fermi–Ulam model. It is confirmed that the mean recurrence time is dependent on the size of the window chosen in the phase space where particles are allowed to return. The fractal dimension of the region is determined by the slope of the recurrence time against the size of the window and two numerical values are measured: (i) [Formula: see text] confirming normal diffusion for chaotic regions far from periodic domains and (ii) [Formula: see text] leading to anomalous diffusion measured inside islands of stability and invariant curves corresponding to regular orbits, a signature of local trapping of an ensemble of particles. The Lyapunov time is the inverse of the Lyapunov exponent. Therefore, the Lyapunov time is measured over different domains in the phase space through a direct determination of the Lyapunov exponent.

中文翻译：

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费米-乌拉姆模型的特征时间

为 Fermi-Ulam 模型测量平均 Poincaré 重现时间和 Lyapunov 时间。已确认平均复发时间取决于在允许粒子返回的相空间中选择的窗口大小。该区域的分形维数由递归时间相对于窗口大小的斜率确定，并测量两个数值：（i）[公式：见文本]确认远离周期性域的混沌区域的正常扩散和（ii ) [公式：见正文] 导致在稳定岛内测量的异常扩散和对应于规则轨道的不变曲线，这是粒子集合的局部捕获的特征。Lyapunov 时间是 Lyapunov 指数的倒数。所以，