论文标题
定向Pinsker代数及其应用
Directional Pinsker algebra and its applications
论文作者
论文摘要
在本文中，我们介绍了方向的Pinsker代数，并构建了偏斜的产品来研究它。作为应用程序，我们表明1。如果具有正方向测量熵的$ \ mathbb {z}^2 $ - 系统，那么它是沿相应方向的多变量定向均值li-yorke混乱； 2。对于$ \ mathbb {z}^2 $ - 系统上的任何ergodic措施，在一组方向渐近造部分的相交中，在方向性渐近造物的一组方向熵元中的相交在一组方向测量措施理论熵段中密集。
In this paper, we introduce the directional Pinsker algebra, and construct a skew product to study it. As applications, we show that 1. if a $\mathbb{Z}^2$-system with positive directional measure-theoretic entropy then it is multivariant directional mean Li-Yorke chaotic along the corresponding direction; 2. for any ergodic measure on a $\mathbb{Z}^2$-system, the intersection of the set of directional measure-theoretic entropy tuples with the set of directional asymptotic tuples is dense in the set of directional measure-theoretic entropy tuples.
