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.

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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