On measure-preserving $\mathbb{F}_p^\omega$-systems of order $k$

Pablo Candela; Diego González-Sánchez; Balázs Szegedy

On measure-preserving $\mathbb{F}_p^\omega$-systems of order $k$

Dynamical Systems 2023-08-15 v1 Combinatorics

Authors: Pablo Candela , Diego González-Sánchez , Balázs Szegedy

Abstract

Building on previous work in the nilspace-theoretic approach to the study of Host-Kra factors of measure-preserving systems, we prove that every ergodic $\mathbb{F}_p^\omega$ -system of order $k$ is a factor of an Abramov $\mathbb{F}_p^\omega$ -system of order $k$ . This answers a question of Jamneshan, Shalom and Tao.

Keywords

measure-preserving systems nilspace theory host-kra factors ergodic systems abramov systems finite fields

Cite

@article{arxiv.2308.06322,
  title  = {On measure-preserving $\mathbb{F}_p^\omega$-systems of order $k$},
  author = {Pablo Candela and Diego González-Sánchez and Balázs Szegedy},
  journal= {arXiv preprint arXiv:2308.06322},
  year   = {2023}
}

Comments

15 pages

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