Distributional Chaos in the Baire Space

TL;DR

This paper investigates distributional chaos in the Baire Space, a non-compact metric dynamical system, showing that certain subshifts exhibit dense distributional chaos.

Contribution

It proves that subshifts of finite type and bounded type in the Baire Space display dense distributional chaos, extending chaos theory to non-compact spaces.

Findings

Subshifts of finite type have dense distributional chaos.

Subshifts of bounded type with perfect and dense periodic points exhibit distributional chaos.

Distributional chaos is established in the Baire Space for specific subshifts.

Abstract

In this paper we consider the question of distributional chaos on non-compact metric dynamical systems. We focus on a shift space over a countable alphabet, the Baire Space. We prove that on the Baire Space subshifts of finite type exhibit dense distributional chaos and subshifts of bounded type that are perfect and have a dense set of periodic points also have distributional chaos.