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.
Recommended Citation
E. Akin and J. Rautio, "Chain Transitive Homeomorphisms on a Space: All or None," Pacific Journal of Mathematics, vol. 291, no. 1, pp. 1 - 49, Mathematical Sciences Publishers (MSP), Jan 2017.
The definitive version is available at https://doi.org/10.2140/pjm.2017.291.1
Department(s)
Mathematics and Statistics
Keywords and Phrases
Chain transitive homeomorphism; Omega set; Rigid space; Slovak space
International Standard Serial Number (ISSN)
0030-8730
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2026 Mathematical Sciences Publishers (MSP), All rights reserved.
Publication Date
01 Jan 2017
