Li–Yorke chaos for composition operators on \(L^p\)-spaces
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Li–Yorke chaos is a popular and well-studied notion of chaos. Several simple and useful characterizations of this notion of chaos in the setting of linear dynamics were obtained recently. In this note we show that even simpler and more useful characterizations of Li–Yorke chaos can be given in the special setting of composition operators on \(L^p\)-spaces. As a consequence we obtain a simple characterization of weighted shifts which are Li–Yorke chaotic. We give numerous examples to show that our results are sharp.
KeywordsLi–Yorke chaos Composition operators \(L^p\)-spaces Weakly wandering sets
Mathematics Subject ClassificationPrimary 47A16 47B33 Secondary 37D45
The authors thank the referee whose valuable comments improved the presentation of the article.
- 8.Grivaux, S., Matheron, É., Menet, Q.: Linear dynamical systems on Hilbert spaces: typical properties and explicity examples. Preprint, arXiv:1703.01854