论文标题
线性混沌图中的相关功能
Correlation functions in linear chaotic maps
论文作者
论文摘要
混乱地图的最简单示例是圆形，圆环或托架产物上的线性，保护区的图。分别称为Bernoulli地图，CAT图和最近引入的“时空”猫图。我们研究这些图中的相关函数。对于Bernoulli映射，我们以多种方式计算相关函数：通过直接计算积分，通过傅立叶序列，通过符号动力学以及通过周期性轨道进行计算。就Perron-Frobenius操作员的本征函数而言，与更标准的处理有关，其中一些方法更简单，也扩展到多点相关函数。对于猫地图，我们通过傅立叶扩展来计算相关功能，审查和扩展克劳福德和卡里对两点功能的先前处理，并讨论阴影的局限性。最后，对于时空猫图（旨在成为多体混乱的模型），我们表明本地操作员的相关功能消失了。
The simplest examples of chaotic maps are linear, area-preserving maps on the circle, torus, or product of tori; respectively known as the Bernoulli map, the cat map, and the recently introduced "spatiotemporal" cat map. We study correlation functions in these maps. For the Bernoulli map, we compute the correlation functions in a variety of ways: by direct computation of the integral, through Fourier series, through symbolic dynamics, and through periodic orbits. In relation to the more standard treatment in terms of eigenfunctions of the Perron-Frobenius operator, some of these methods are simpler and also extend to multipoint correlation functions. For the cat map, we compute correlation functions through a Fourier expansion, review and expand on a prior treatment of two-point functions by Crawford and Cary, and discuss the limitations of shadowing. Finally, for the spatiotemporal cat map -- intended to be a model of many-body chaos -- we show that connected correlation functions of local operators vanish.
