标题： 递推与粘性在噪声哈珀映射中 显示英文标题

标题： Recurrence and Stickiness in the Noisy Harper Map

摘要： 当三种类型的噪声引入到保面积的Harper映射中时，庞加莱返回统计（PRS）表现出一个扩展的尾部，对应于更长返回时间的概率增加。 对于具有规则轨道和混沌轨道混合的确定性情况，规则岛屿导致返回分布中的幂律衰减。 噪声扰动使得轨迹能够进入岛屿内部，并且这可以增强它们的捕获效应，导致许多轨道需要更长时间才能返回到其初始条件的邻域，从而在中间时间尺度上导致较慢的幂律衰减。 然而，在更长的时间尺度上，噪声的PRS表现出指数衰减，最终低于确定性的PRS。 我们将捕获时间和访问岛屿的时间分布与返回时间进行比较，以说明噪声在产生PRS尾部中的重要性。 一个简单的动力学模型——具有三个状态的马尔可夫链——展示了噪声允许进入以前不可到达的岛屿如何导致较慢的衰减。 显示英文摘要

摘要： When three types of noise are introduced to the area-preserving Harper map, the Poincar\'e recurrence statistic (PRS) exhibits an extended tail, corresponding to an increased probability of longer recurrence times. For a deterministic case with a mixture of regular and chaotic orbits, regular islands are responsible for a power-law decay in the recurrence distribution. Noise perturbations allow trajectories to access the interior of the islands, and this can enhance their trapping effect, causing many orbits to take longer to return to a neighborhood of their initial conditions and resulting in a slower power-law decay on an intermediate time scale. On a longer time scale, however, the noisy PRS exhibits exponential decay, eventually falling below the deterministic PRS. We compare distributions of trapping and visit times to islands with recurrence times to show the importance of noise in creating tails in the PRS. A simple model of the dynamics -- a Markov chain with three states -- demonstrates how the slower decay can be caused by noise allowing entry to a previously inaccessible island.