Stronger versions of sensitivity for minimal group actions

TL;DR

This paper investigates enhanced forms of sensitivity in minimal group actions, such as $n$-sensitivity and thick $n$-sensitivity, and characterizes these properties through the regionally proximal relation.

Contribution

It introduces and characterizes new stronger sensitivity notions in minimal group actions, expanding understanding of their dynamical properties.

Findings

Characterization of $n$-sensitivity via the regionally proximal relation

Introduction of thick $n$-sensitivity and blockily thick $n$-sensitivity

Establishment of relationships between sensitivity variants and proximal relations

Abstract

We study several stronger versions of sensitivity for minimal group actions, including $n$-sensitivity, thick $n$-sensitivity and blockily thick $n$-sensitivity, and characterize them by the regionally proximal relation.