ENTROPY DIMENSION OF MEASURE PRESERVING SYSTEMS
ENTROPY DIMENSION OF MEASURE PRESERVING SYSTEMS
复制标题
测量保存系统的熵维
DOI：
10.1090/tran/7542
复制
发表时间：
2019
影响因子：
1.3
通讯作者：
Park Kyewon Koh
中科院分区：
文献类型：
--
作者：
Dou Dou;Huang Wen;Park Kyewon Koh
引入度量熵维的概念来度量零熵动力系统的复杂度。对于测度保持系统，我们通过熵产生序列的维数来定义熵维。这种组合方法为我们分析熵零系统提供了一种新的见解。我们还定义了系统的维集来研究系统中各因素的随机性结构。作为正熵情况下k系统的推广，引入了熵零系统中一致维的概念。研究了熵零系统之间的连接性，并利用维数集证明了若干类熵零系统之间的不连接性。给定一个拓扑系统，我们比较了拓扑熵维和度量熵维。参考文献
The notion of metric entropy dimension is introduced to measure the complexity of entropy zero dynamical systems. For measure preserving systems, we define entropy dimension via the dimension of entropy generating sequences. This combinatorial approach provides us with a new insight for analyzing entropy zero systems. We also define the dimension set of a system to investigate the structure of the randomness of the factors of a system. The notion of a uniform dimension in the class of entropy zero systems is introduced as a generalization of a K-system in the case of positive entropy. We investigate joinings among entropy zero systems and prove the disjointness property among some classes of entropy zero systems using dimension sets. Given a topological system, we compare topological entropy dimension with metric entropy dimension. References