论文标题
相对慢熵
Relative slow entropy
论文作者
论文摘要
1997年，Katok- Thouvenot和Ferenczi独立地引入了``慢熵''的概念，作为将测量保护系统与零熵进行定量比较的方法。我们为以给定因素为条件的量度保留系统开发了该理论的相对版本。我们的新定义继承了许多理想的特性，使其成为Katok-Thouvenot/Ferenczi理论和经典条件的Kolmogorov--Sinai熵的自然概括。作为一个应用程序，我们证明了Ferenczi结果的相对版本，该结果根据其慢速熵对等距系统进行了分类。我们还为刚性扩展的概念引入了一个新的定义，并研究了其与相对慢熵的关系。
In 1997, Katok--Thouvenot and Ferenczi independently introduced a notion of ``slow entropy'' as a way to quantitatively compare measure-preserving systems with zero entropy. We develop a relative version of this theory for a measure-preserving system conditioned on a given factor. Our new definition inherits many desirable properties that make it a natural generalization of both the Katok--Thouvenot/Ferenczi theory and the classical conditional Kolmogorov--Sinai entropy. As an application, we prove a relative version of a result of Ferenczi that classifies isometric systems in terms of their slow entropy. We also introduce a new definition for the notion of a rigid extension and investigate its relationship to relative slow entropy.
