Li-Yorke Chaos for Composition Operators on $L^p$-Spaces

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 $L^p$ 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.

References in corpus (1)

• Expansivity and Shadowing in Linear Dynamics

Cited by in corpus (6)

• Chaos and frequent hypercyclicity for composition operators
• Linear Dynamics Induced by Odometers
• Generalized Hyperbolicity and Shadowing in $L^p$ spaces
• Dynamical properties for composition operators on $H^2({\mathbb{C}}_{+})$
• Dynamics for affine composition operators on weighted Bergman space of a half plane
• Shift-like Operators on $L^p(X)$