Vol. 291, No. 1, 2017

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Chain transitive homeomorphisms on a space: all or none

Ethan Akin and Juho Rautio

Vol. 291 (2017), No. 1, 1–49

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.

omega set, chain transitive homeomorphism, rigid space, Slovak space
Mathematical Subject Classification 2010
Primary: 37B20, 37B25
Received: 2 December 2015
Revised: 3 February 2017
Accepted: 20 March 2017
Published: 20 August 2017
Ethan Akin
Mathematics Department
The City College
New York, NY
United States
Juho Rautio
Department of Mathematical Sciences
University of Oulu