On Pinsker factors for Rokhlin entropy

TL;DR

This paper proves the existence and uniqueness of the Pinsker factor with zero Rokhlin entropy for any dynamical system, and characterizes ergodic systems with atomless Pinsker factors as relatively weakly mixing extensions.

Contribution

It establishes the existence, uniqueness, and properties of Pinsker factors in systems with Rokhlin entropy, extending the understanding of entropy in dynamical systems.

Findings

Existence and uniqueness of the Pinsker factor with zero Rokhlin entropy.

Ergodic systems with atomless Pinsker factors are relatively weakly mixing extensions.

Characterization of systems based on the structure of their Pinsker factor.

Abstract

In this paper we will prove that any dynamical system posess the unique maximal factor of zero Rokhlin entropy, so-called Pinsker factor. It is proven also, that if the system is ergodic and this factor has no atoms then system is relatively weakly mixing extension of its Pinsker factor.