The interplay between recurrence and hypercyclicity in dissipative contexts
Dynamical Systems
2023-03-20 v1 Functional Analysis
Abstract
Motivated by recent investigations \cite{Costakis, Bonilla} on the notion of recurrence in linear dynamics, we deepen into the notions of recurrence and frequent recurrence in the setting of dissipative composition operators with bounded distortion, a class of linear operators which includes backward shifts. Among other results, we show that these two notions are, actually, equivalent to those of hypercyclicity and frequent hypercyclicity, respectively. More particularly, we improve \cite[Theorem 5.2]{Bonilla} and, also, provide an answer to an open question posed in \cite[Question 5.3]{Bonilla}.
Keywords
Cite
@article{arxiv.2303.09837,
title = {The interplay between recurrence and hypercyclicity in dissipative contexts},
author = {E. D'Aniello and M. Maiuriello and J. B. Seoane Sepulveda},
journal= {arXiv preprint arXiv:2303.09837},
year = {2023}
}