Li-Yorke Chaos for Composition Operators on $L^p$-Spaces
Dynamical Systems
2023-05-09 v1
Abstract
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 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.
Keywords
Cite
@article{arxiv.1810.04210,
title = {Li-Yorke Chaos for Composition Operators on $L^p$-Spaces},
author = {N. C. Bernardes and U. B. Darji and B. Pires},
journal= {arXiv preprint arXiv:1810.04210},
year = {2023}
}