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Chain transitive
homeomorphisms on a space: all or none
Ethan Akin and Juho Rautio |
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Vol. 291 (2017), No. 1, 1–49
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Abstract |
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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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Keywords
omega set, chain transitive homeomorphism, rigid space,
Slovak space
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Mathematical Subject Classification 2010
Primary: 37B20, 37B25
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Milestones
Received: 2 December 2015
Revised: 3 February 2017
Accepted: 20 March 2017
Published: 20 August 2017
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Authors |
| Ethan Akin | |
| Mathematics Department The City College New York, NY United States |
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| Juho Rautio | |
| Department of Mathematical
Sciences University of Oulu Finland |
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