Abstract
There are several different common definitions of a property in topological dynamics called "topological transitivity," and it is part of the folklore of dynamical systems that under reasonable hypotheses, they are equivalent. Various equivalences are proved in different places, but the full story is difficult to find. This note provides a complete description of the relationships among the different properties. © 2012 Elsevier B.V.
Recommended Citation
E. Akin and J. D. Carlson, "Conceptions of Topological Transitivity," Topology and Its Applications, vol. 159, no. 12, pp. 2815 - 2830, Elsevier, Aug 2012.
The definitive version is available at https://doi.org/10.1016/j.topol.2012.04.016
Department(s)
Mathematics and Statistics
Publication Status
Open Archive
Keywords and Phrases
Isolated points; Minimal sets; Topological transitivity; Transitive points
International Standard Serial Number (ISSN)
0166-8641
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2026 Elsevier, All rights reserved.
Publication Date
01 Aug 2012
