Chain transitive homeomorphisms on a space: all or none

TL;DR

This paper investigates the types of topological spaces that can serve as omega limit sets for discrete dynamical systems, focusing on the existence and universality of chain transitive homeomorphisms.

Contribution

It characterizes spaces that admit chain transitive homeomorphisms and identifies spaces where all homeomorphisms are chain transitive.

Findings

Identifies spaces that can be omega limit sets of dynamical systems

Determines conditions under which all homeomorphisms are chain transitive

Provides classifications for spaces based on chain transitivity properties

Abstract

We consider which spaces can be realized as the omega limit set of the discrete time dynamical system. This is equivalent to asking which spaces admit a chain transitive homeomorphism and which do not. This leads us to ask for spaces where all homeomorphisms are chain transitive.