Distributional Chaos and Dendrites

TL;DR

This paper investigates distributional chaos in dendrites, comparing its different types and their distinctions from chaos in simpler spaces, and explores correlations with other chaos types.

Contribution

It analyzes the distinctions among distributional chaos types on dendrites, extending understanding beyond interval spaces and examining their relation to other chaos forms.

Findings

Distributional chaos types are distinguishable on dendrites.

Differences among chaos types are more pronounced in complex spaces.

Correlation with other chaos types is briefly examined.

Abstract

Many definitions of chaos have appeared in the last decades and with them the question if they are equivalent in some more specific spaces. Our focus will be distributional chaos, first defined in 1994 and later subdivided into three major types (and even more subtypes). These versions of chaos are equivalent on a closed interval, but distinct in more complicated spaces. Since dendrites have much in common with the interval, we explore whether or not we can distinguish these kinds of chaos already on dendrites. In the end of the paper we will also briefly look at the correlation with other types of chaos.