Host-Kra theory for $\bigoplus_{p\in P}\mathbb{F}_p$- Systems and multiple recurrence

Or Shalom

doi:10.1017/etds.2021.109

Host-Kra theory for $\bigoplus_{p\in P}\mathbb{F}_p$- Systems and multiple recurrence

Dynamical Systems 2022-02-15 v3

Authors: Or Shalom

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Abstract

Let $\mathcal{P}$ be an (unbounded) countable multiset of primes (i.e. every prime may appear multiple times) and let $G=\bigoplus_{p\in \mathcal{P}}\mathbb{F}_p$ . We develop a Host-Kra structure theory for the universal characteristic factors of an ergodic $G$ -system. More specifically, we generalize the main results of Bergelson Tao and Ziegler who studied these factors in the special case $\mathcal{P}=\{p,p,p,...\}$ for some fixed prime $p$ . As an application we deduce a Khintchine-type recurrence theorem in the flavor of Bergelson Tao and Ziegler and Bergelson Host and Kra.

Keywords

host-kra theory ergodic systems characteristic factors multiple recurrence prime multiset khintchine-type theorem

Cite

@article{arxiv.2101.04613,
  title  = {Host-Kra theory for $\bigoplus_{p\in P}\mathbb{F}_p$- Systems and multiple recurrence},
  author = {Or Shalom},
  journal= {arXiv preprint arXiv:2101.04613},
  year   = {2022}
}

Comments

65 pages. Added an acknowledgement. This is the final accepted version appeared in Ergodic Theory and Dynamical Systems. arXiv admin note: substantial text overlap with arXiv:2006.06470

Host-Kra theory for $\bigoplus_{p\in P}\mathbb{F}_p$- Systems and multiple recurrence

Abstract

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