2023/03/17 by Emma D’Aniello, D'Aniello, E., M. Maiuriello +3 · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2303.09837
openalex publication_date 2023/03/17 · openalex created_date 2023/03/21 · openalex updated_date 2026/07/28
Motivated by recent investigations \citeCostakis, 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.