University of Oulu

Akin, E., Rautio, J. (2017) Chain transitive homeomorphisms on a space: all or none. Pacific Journal of Mathematics, 291 (1), 1-49. doi:10.2140/pjm.2017.291.1

Chain transitive homeomorphisms on a space : all or none

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Author: Akin, Ethan1; Rautio, Juho2
Organizations: 1Mathematics Department, The City College, New York, NY United States
2Department of Mathematical Sciences, University of Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.4 MB)
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Language: English
Published: Mathematical Sciences Publishers, 2017
Publish Date: 2019-03-28


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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Series: Pacific journal of mathematics
ISSN: 0030-8730
ISSN-E: 0030-8730
ISSN-L: 0030-8730
Volume: 291
Issue: 1
Pages: 1 - 49
DOI: 10.2140/pjm.2017.291.1
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Copyright information: © Copyright 2017 Pacific Journal of Mathematics. All rights reserved.