# Distributionally chaotic maps are $C^0$-dense

## TL;DR

This paper proves that continuous maps exhibiting distributional chaos of type 1 are densely present in the space of all continuous self-maps on any compact topological manifold, highlighting the prevalence of chaotic behavior.

## Contribution

It establishes the $C^0$-density of DC1 maps in the space of continuous self-maps on compact manifolds, extending understanding of chaos distribution.

## Key findings

- DC1 maps are $C^0$-dense in continuous self-maps
- Chaotic behavior is prevalent in compact manifolds
- Extends previous results on distributional chaos

## Abstract

We prove that the set of maps which exhibit distributional chaos of type 1 (DC1) is $C^0$-dense in the space of continuous self-maps of given any compact topological manifold (possibly with boundary).