Chaotic dynamics of minimal center of attraction for a flow with discrete amenable phase group

TL;DR

This paper investigates chaotic behaviors near minimal centers of attraction in dynamical systems where an infinite amenable group acts on a compact metric space, revealing complex dynamics influenced by the group's properties.

Contribution

It introduces a new analysis of chaos in systems with discrete amenable group actions, focusing on minimal centers of attraction and F{\

Findings

Chaotic dynamics are present near minimal centers of attraction.

The study extends understanding of group actions in topological dynamics.

Results highlight the influence of amenability on chaos emergence.

Abstract

Let $G$ be a discrete infinite amenable group, which acts from the left on a compact metric space $X$. In this paper, we study the chaotic dynamics exhibited inside and near a minimal center of attraction of $(G,X)$ relative to any F{\o}lner net in $G$.