Topological chaos: what may this mean ?

TL;DR

This paper examines various topological properties associated with chaos in dynamical systems, distinguishing between overall and partial chaos, and analyzing the relative chaos of different properties without proposing new definitions.

Contribution

It provides a theoretical overview of chaos in topological dynamics, emphasizing distinctions and hierarchies among chaotic properties without introducing new chaos definitions.

Findings

Distinction between overall chaos and partial chaos

Some properties are more chaotic than others

No new chaos definitions are proposed

Abstract

We confront existing definitions of chaos with the state of the art in topological dynamics. The article does not propose any new definition of chaos but, starting from several topological properties that can be reasonably called chaotic, tries to sketch a theoretical view of chaos. Among the main ideas in this article are the distinction between overall chaos and partial chaos, and the fact that some dynamical properties may be considered more chaotic than others.