论文标题
混沌系统中的大偏差：精确的结果和动态相变
Large deviations in chaotic systems: exact results and dynamical phase transition
论文作者
论文摘要
混沌动力学的巨大偏差具有潜在的重大和巨大的后果。我们研究了混乱地图产生的一系列有限长度$ n $的大偏差。分布通常显示出具有$ n $的指数衰减，与大差异（速率）功能相关。我们在分析上获得了加倍，帐篷和逻辑图的确切速率函数。对于后两个，将解决方案作为功率序列给出，其系数可以系统地计算为任何顺序。我们还从数值上获得了CAT图的速率函数，从而发现了有很大的奇异性的有力证据，我们将其解释为二阶动力学相变。此外，如果混乱的图不是可逆的，我们开发了一个数值工具，用于有效地模拟序列的非典型实现，并将其应用于帐篷和逻辑图。
Large deviations in chaotic dynamics have potentially significant and dramatic consequences. We study large deviations of series of finite lengths $N$ generated by chaotic maps. The distributions generally display an exponential decay with $N$, associated with large-deviation (rate) functions. We obtain the exact rate functions analytically for the doubling, tent, and logistic maps. For the latter two, the solution is given as a power series whose coefficients can be systematically calculated to any order. We also obtain the rate function for the cat map numerically, uncovering strong evidence for the existence of a remarkable singularity of it that we interpret as a second order dynamical phase transition. Furthermore, we develop a numerical tool for efficiently simulating atypical realizations of sequences if the chaotic map is not invertible, and we apply it to the tent and logistic maps.
