A view on multiple recurrence
Dynamical Systems
2022-08-23 v3 Combinatorics
Functional Analysis
Abstract
In this note we present a proof of multiple recurrence for ergodic systems (and thereby of Szemer\'edi's theorem) being a mixture of three known proofs. It is based on a conditional version of the Jacobs-de Leeuw-Glicksberg decomposition and properties of the Gowers-Host-Kra uniformity seminorms.
Cite
@article{arxiv.2201.02096,
title = {A view on multiple recurrence},
author = {Tanja Eisner},
journal= {arXiv preprint arXiv:2201.02096},
year = {2022}
}
Comments
18 pages. The proof has been considerably simplified and shortened by avoiding the use of the fact that the Host-Kra-Ziegler factors are factors. The only information needed on the corresponding subspaces is their description via the Gowers-Host-Kra seminorms