Recurrence for stationary group actions

TL;DR

This paper extends multiple recurrence results to general stationary dynamical systems using a structure theorem, demonstrating that sets of positive measure exhibit recurrence properties.

Contribution

It introduces a recurrence theorem for stationary actions based on a structure theorem from prior work, broadening the scope of recurrence results.

Findings

Proves multiple recurrence in stationary systems

Utilizes a structure theorem from [FG2010]

Establishes recurrence for positive measure sets

Abstract

Using a structure theorem from [FG2010] we prove a version of multiple recurrence for sets of positive measure in a general stationary dynamical system.