Directional Pinsker algebra and its applications

Abstract

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.

References in corpus (7)

• Recent development of chaos theory in topological dynamics
• Stable sets and mean Li-Yorke chaos in positive entropy systems
• Mean Li-Yorke chaos along some good sequences
• Positive entropy implies chaos along any infinite sequence
• Directional recurrence and directional rigidity for infinite measure preserving actions of nilpotent lattices
• Directional Kronecker algebra for ${\mathbb{Z}}^q$-actions
• Pinsker $\sigma$-algebra Character and mean Li-Yorke chaos