论文标题
Chebyshev动力学系统及其概括的区别相关性能
Distinguished correlation properties of Chebyshev dynamical systems and their generalisations
论文作者
论文摘要
我们表明，在所有光滑的一维图中，在N- ary偏移（n个符号的伯努利偏移）中，Chebyshev地图的区分是从最小的高阶相关性来区分。我们概括了我们的考虑并研究了一个转移的Chebyshev地图家族，为两点和高阶相关函数提供了分析结果。我们还审查了n-ther Chebyshev地图的Perron-Frobenius操作员的特征值和特征函数的结果。对于奇数N而言，频谱是退化的。最后，我们考虑了移动的Chebyshev映射的耦合地图晶格（CML），并数值研究了时间和空间最近的近近纽布相关性的零，这在混乱量化的场理论中具有兴趣。
We show that, among all smooth one-dimensional maps conjugated to an N-ary shift (a Bernoulli shift of N symbols), Chebyshev maps are distinguished in the sense that they have least higher-order correlations. We generalise our consideration and study a family of shifted Chebyshev maps, presenting analytic results for two-point and higher-order correlation functions. We also review results for the eigenvalues and eigenfunctions of the Perron-Frobenius operator of N-th order Chebyshev maps and their shifted generalisations. The spectrum is degenerate for odd N. Finally, we consider coupled map lattices (CMLs) of shifted Chebyshev maps and numerically investigate zeros of the temporal and spatial nearest-neighbour correlations, which are of interest in chaotically quantized field theories.
