Examines supercyclicity and hypercyclicity in composition operators on measurable functions, suggesting new insights into their behavior.
We study the dynamical properties of composition operators acting on Banach spaces of measurable functions. In particular, we study in some detail the composition operators induced by odometers, which allows us to give a variety of new examples and counter-examples. We also get general statements about supercyclicity and frequent hypercyclicity of composition operators on Lₚ-spaces.
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Bayart et al. (2026) studied this question.
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