We study different pointwise recurrence notions for linear dynamical systems from the
Ergodic Theory point of view. We show that from any reiteratively recurrent vector x 0, for an …

We study multiply recurrent and hypercyclic operators as a special case of $\mathcal F $-
hypercyclicity, where $\mathcal F $ is the family of subsets of the natural numbers containing …

We introduce and study the notion of hereditary frequent hypercyclicity, which is a
reinforcement of the well known concept of frequent hypercyclicity. This notion is useful for …

We characterize chaotic linear operators on reflexive Banach spaces in terms of the
existence of long arithmetic progressions in the sets of return times. We also show that this …

We study, for a continuous linear operator T on an F-space X, when the direct sum operator
T⊕ T is recurrent on X⊕ X. In particular: we establish the analogous notion, for recurrence …

We study recurrence and the related $\mathscr P_\mathcal F $ property for linear operators
on Banach spaces. We show that for special families, called block families, hypercyclic …

This expository survey is dedicated to recent developments in the area of linear dynamics.
Topics include frequent hypercyclicity, $\mathcal {U} $-frequent hypercyclicity, reiterative …

Given a dynamical system $(X, T) $ and a family $\mathsf {I}\subseteq\mathcal {P}(\omega) $
of" small" sets of nonnegative integers, a point $ x\in X $ is said to be $\mathsf {I} $-strong …

We provide with criteria for a family of sequences of operators to share a frequently universal
vector. These criteria are inspired by the classical Frequent Hypercyclicity Criterion and by a …

Disjoint hypercyclicity, Sidon sets and weakly mixing operators Page 1 Ergod. Th. & Dynam.
Sys., page 1 of 15 © The Author(s), 2023. Published by Cambridge University Press. doi:10.1017/etds.2023.54 …