论文标题
某些组合构造的慢熵
Slow entropy of some combinatorial constructions
论文作者
论文摘要
与经典测度熵相比，测量理论慢熵是一种更精致的不变性，该理论熵表征了具有可分辨轨道类型的亚指数增长率的动态系统的复杂性。在本文中，我们证明了刚性变换的上和下多项式慢熵值的灵活性结果，以及地图承认良好的循环近似值。此外，我们表明，对于有限等级系统的较低度量慢熵熵不存在一般上限。
Measure-theoretic slow entropy is a more refined invariant than the classical measure-theoretic entropy to characterize the complexity of dynamical systems with subexponential growth rates of distinguishable orbit types. In this paper we prove flexibility results for the values of upper and lower polynomial slow entropy of rigid transformations as well as maps admitting a good cyclic approximation. Moreover, we show that there cannot exist a general upper bound on the lower measure-theoretic slow entropy for systems of finite rank.
