Localization of mixing property via Furstenberg families

TL;DR

This paper investigates how mixing properties in dynamical systems can be localized using Furstenberg families, demonstrating the existence of specific mixing sets in systems with positive entropy and non-PI minimal systems.

Contribution

It introduces the concept of localizing mixing properties via Furstenberg families and proves the existence of such mixing sets in particular classes of dynamical systems.

Findings

Existence of $\

Existence of $\

Abstract

This paper is devoted to studying the localization of mixing property via Furstenberg families. It is shown that there exists some $\mathscr{F}_{pubd}$-mixing set in every dynamical system with positive entropy, and some $\mathscr{F}_{ps}$-mixing set in every non-PI minimal system.