Chain transitive homeomorphisms on a space : all or none

Abstract

<div lang="en" class="abs"><p class="abs_header">Abstract</p><p>Extending earlier work, we consider when a compact metric space can be realized as the omega limit set of a discrete time dynamical system. This is equivalent to asking when the space admits a chain transitive homeomorphism. We approach this problem in terms of various conditions on the connected components of the space. We also construct spaces where all homeomorphisms are chain transitive.</p></div>