关于修正功率熵的几点注记
Some remarks on modified power entropy
摘要：
本文的目的是指出关于$\Z$ -和$\N$ -作用的修正功率熵的一些观察。首先，我们提供了一个基本的例子表明，这个量是敏感的瞬态动力学，因此不满足变分原理。此外，我们表明，修改后的功率熵是不适合检测的过程中发生的几乎周期的几乎自守极小系统的过渡等度连续性的突破。在这方面，它不同于功率熵和无定形复杂性，这是零熵系统（“慢熵”）的两个进一步的拓扑不变量。最后，我们构造了一个零修正幂熵的不规则Toeplitz流的例子。
英文摘要：
The aim of this note is to point out some observations concerning modified power entropy of $\Z$- and $\N$-actions. First, we provide an elementary example showing that this quantity is sensitive to transient dynamics, and therefore does not satisfy a variational principle. Further, we show that modified power entropy is not suitable to detect the break of equicontinuity which takes place during the transition from almost periodic to almost automorphic minimal systems. In this respect, it differs from power entropy and amorphic complexity, which are two further topological invariants for zero entropy systems (`slow entropies'). Finally, we construct an example of an irregular Toeplitz flow with zero modified power entropy.
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