# Devaney chaos, Li-Yorke chaos, and multi-dimensional Li-Yorke chaos for topological dynamics

## TL;DR

This paper investigates different forms of chaos, including Devaney and Li-Yorke chaos, within the context of topological group or semigroup actions, providing a comprehensive analysis of chaotic behaviors.

## Contribution

It introduces new insights into chaos types in topological dynamics, focusing on group and semigroup actions, and explores their interrelations.

## Key findings

- Characterization of Devaney chaos in topological actions
- Conditions for Li-Yorke chaos in semigroup actions
- Analysis of multi-dimensional Li-Yorke chaos

## Abstract

In this paper, we study various chaos of topological group or semigroup actions.