Directional Pinsker algebra and its applications

In this paper, we introduce the directional Pinsker algebra, and construct a skew product to study it. As applications, we show that (i) if a Z2-system with positive directional measure-theoretic entropy then it is multivariant directional mean Li–Yorke chaotic along the corresponding direction; (ii) for any ergodic measure on a Z2-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.