#### Vol. 291, No. 1, 2017

 Recent Issues Vol. 317: 1 Vol. 316: 1  2 Vol. 315: 1  2 Vol. 314: 1  2 Vol. 313: 1  2 Vol. 312: 1  2 Vol. 311: 1  2 Vol. 310: 1  2 Online Archive Volume: Issue:
 The Journal Subscriptions Editorial Board Officers Contacts Submission Guidelines Submission Form Policies for Authors ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Special Issues Author Index To Appear Other MSP Journals
Chain transitive homeomorphisms on a space: all or none

### Ethan Akin and Juho Rautio

Vol. 291 (2017), No. 1, 1–49
##### 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