Idempotent ultrafilters and polynomial recurrence

TL;DR

This paper presents a novel proof of a polynomial recurrence theorem by employing idempotent ultrafilters, offering an alternative approach to the traditional IP-limit method.

Contribution

It introduces the use of idempotent ultrafilters as a new technique to prove polynomial recurrence results, replacing the conventional IP-limit approach.

Findings

New proof of polynomial recurrence using ultrafilters

Demonstrates the effectiveness of ultrafilters in ergodic theory

Provides insights into ultrafilter-based methods in recurrence theory

Abstract

We give a new proof of a polynomial recurrence result due to Bergelson, Furstenberg, and McCutcheon, using idempotent ultrafilters instead of IP-limits.