Sufficient Conditions under Which a Transitive System is Chaotic
Abstract
Let (X,T) be a topologically transitive dynamical system. We show that if there is a subsystem (Y,T) of (X,T) such that (X x Y,T x T) is transitive, then (X,T) is strongly chaotic in the sense of Li and Yorke. We then show that many of the known sufficient conditions in the literature, as well as a few new results, are corollaries of this statement. In fact, the kind of chaotic behavior we deduce in these results is a much stronger variant of Li-Yorke chaos which we call uniform chaos. For minimal systems we show, among other results, that uniform chaos is preserved by extensions and that a minimal system which is not uniformly chaotic is PI. © 2009 Cambridge University Press.
Recommended Citation
E. Akin et al., "Sufficient Conditions under Which a Transitive System is Chaotic," Ergodic Theory and Dynamical Systems, vol. 30, no. 5, pp. 1277 - 1310, Cambridge University Press, Oct 2010.
The definitive version is available at https://doi.org/10.1017/S0143385709000753
Department(s)
Mathematics and Statistics
International Standard Serial Number (ISSN)
1469-4417; 0143-3857
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2026 Cambridge University Press, All rights reserved.
Publication Date
01 Oct 2010
