On Local Rank, Joinings and Asymptotic Properties of Measure-Preserving Actions

TL;DR

This paper explores properties of locally rank one measure-preserving actions, discussing related constructions and connecting various results in ergodic theory to deepen understanding of their asymptotic behaviors.

Contribution

It compiles and analyzes facts and constructions related to locally rank one actions, extending previous results by notable researchers in ergodic theory.

Findings

Insights into the structure of locally rank one actions

Connections between joinings and asymptotic properties

Extensions of results by Downarowicz, Katok, and others

Abstract

The note contains a collection of facts and observations around locally rank one actions as well as constructions connected with some results by T.Downarowicz, A.Katok, J.King, F.Parreau, A.A.Prikhodko, E.Roy, J.Serafin, J-P.Thouvenot et al.