遍历理论与可视化。II。调和中时图可视化（准）周期集
Ergodic theory and visualization. II. Harmonic mesochronic plots visualize (quasi)periodic sets
摘要：
本文基于频率分析和遍历理论，提出了一种分析保测度动力系统的新方法，推广了我们的工作[1]。我们的方法采用了谐波时间平均的新概念[2]，并实现为一种计算算法，用于可视化相空间中的周期和准周期集或任意周期性。除了识别所有的周期集，我们的方法是有用的，在检测混沌相空间区域具有良好的精度。该方法的适用范围是用著名的Chirikov标准映射来说明的，而它的全部潜力是通过研究高维测度保持系统，特别是Froeschlé映射和扩展的标准映射。
英文摘要：
We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets or arbitrary periodicity in the phase space. Besides identifying all periodic sets, our method is useful in detecting chaotic phase space regions with a good precision. The range of method's applicability is illustrated using well-known Chirikov standard map, while its full potential is presented by studying higher-dimensional measure-preserving systems, in particular Froeschlé map and extended standard map.
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