PreprintCC BY-NC-ND 4.0HAL
On the dynamics of composition operators: supercyclicity, odometers and translations
Abstract
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.
Related
- Weighted composition operators on the Fock space
- Convexity of the Berezin range of composition operators induced by automorphisms of the Unit Ball in ℂn
- Weighted composition--differentiation operators on mixed-norm, derivative Hardy and F(p,q,s) spaces
- Schatten class membership of products of composition operators and their adjoints
- Compact linear combination of composition operators on weighted Bergman-Orlicz spaces induced by doubling weights
BibTeX
@misc{bayart2026dynamics,
title = {{On the dynamics of composition operators: supercyclicity, odometers and translations}},
author = {Frédéric Bayart and Etienne Matheron},
howpublished = {HAL},
year = {2026},
month = oct,
eprint = {2605.23736},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05630236v2},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - On the dynamics of composition operators: supercyclicity, odometers and translations
AU - Frédéric Bayart
AU - Etienne Matheron
PY - 2026
DA - 2026/10/22
PB - HAL
UR - https://hal.science/hal-05630236v2
AB - 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 L_p-spaces.
ER -