Chain transitive homeomorphisms on a space: all or none

Ethan Akin and Juho Rautio

Vol. 291 (2017), No. 1, 1–49

DOI: 10.2140/pjm.2017.291.1

Abstract

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.

Keywords

omega set, chain transitive homeomorphism, rigid space, Slovak space

Mathematical Subject Classification 2010

Primary: 37B20, 37B25

Milestones

Received: 2 December 2015

Revised: 3 February 2017

Accepted: 20 March 2017

Published: 20 August 2017