Motivated by a recent investigation of Costakis et al. on the notion of recurrence in linear
dynamics, we study various stronger forms of recurrence for linear operators, in particular …

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 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 solve in the negative two open problems, related to the linear and topological structure
of the set of recurrent vectors, asked by Sophie Grivaux, Alfred Peris and the first author of …

We solve in the negative two open problems, related to the linear and topological structure
of the set of recurrent vectors, asked by Sophie Grivaux, Alfred Peris and the first author of …

We study several notions of chaos for hyperspace dynamics associated to continuous linear
operators. More precisely, we consider a continuous linear operator T: X → XT: X→ X on a …

In this article J ℱ-class operators are introduced and some basic properties of J ℱ-vectors
are given. The J ℱ-class operators include the J-class operators and J mix-class operators …

An operator T acting on a Banach space X is said to be super-recurrent if for each open
subset U of X, there exist λ∈ K and n∈ N such that λ T n (U)∩ U≠∅. In this paper, we …