Chebyshev动力系统的特殊关联性质及其推广
Distinguished correlation properties of Chebyshev dynamical systems and their generalisations
摘要：
我们表明，在所有光滑的一维映射共轭的N元移位（伯努利移位的N个符号），切比雪夫映射的区别，在这个意义上，他们有最少的高阶相关性。我们概括我们的考虑和研究家庭的转移切比雪夫映射，两点和高阶相关函数的分析结果。我们还回顾了N阶Chebyshev映射的Perron-Frobenius算子的本征值和本征函数的结果及其移位推广。对于奇数N，谱是简并的。最后，我们考虑耦合映射格子（CML）的移位切比雪夫映射和数值研究的时间和空间的最近邻相关，这是在混沌量子化域论的兴趣的零。
英文摘要：
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.
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