On Li--Yorke chaotic transformation groups modulo an ideal

TL;DR

This paper introduces the concept of Li-Yorke chaos modulo an ideal in topological transformation semigroups, characterizes certain abelian infinite chaotic groups, and explores their decomposability.

Contribution

It defines Li-Yorke chaos modulo an ideal and characterizes a class of abelian infinite chaotic transformation groups with new properties.

Findings

Characterization of abelian infinite Li-Yorke chaotic groups

Elements of this class are co-decomposable into non-chaotic groups

Introduction of the notion of chaos modulo an ideal in semigroups

Abstract

In the following text we introduce the notion of chaoticity modulo an ideal in the sense of Li-Yorke in topological transformation semigroups and bring some of its elementary properties. We continue our study by characterizing a class of abelian infinite Li-Yorke chaotic Fort transformation groups and show all of the elements of the above class is co-decomposable to non-Li-Yorke chaotic transformation groups.