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Growth of hypercyclic functions: a continuous path between $\mathcal{U}$-frequent hypercyclicity and hypercyclicity

Published online by Cambridge University Press:  08 May 2024

Augustin Mouze*
CNRS, UMR 8524 - Laboratoire Paul Painlevé, École Centrale de Lille, Univ. Lille, Lille, France
Vincent Munnier
Lycée Jacques Prévert, Boulogne Billancourt, France
Corresponding author: Augustin Mouze, email:


We are interested in the optimal growth in terms of Lp-averages of hypercyclic and $\mathcal{U}$-frequently hypercyclic functions for some weighted Taylor shift operators acting on the space of analytic functions on the unit disc. We unify the results obtained by considering intermediate notions of upper frequent hypercyclicity between $\mathcal{U}$-frequent hypercyclicity and hypercyclicity.

Research Article
© The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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