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 …

In this paper, we introduce and study the notion of weak recurrence on a Banach space X. In
one hand, we prove some properties of this class of operators. On the other hand, we study …

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 …

In this paper, we introduce and study the notion of super-recurrence of operators. We
investigate some properties of this class of operators and show that it shares some …

In the present work we study the concepts of shadowing and chain recurrence in the setting
of linear dynamics. We prove that shadowing and finite shadowing always coincide for …

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 …

Li–Yorke chaos is a popular and well-studied notion of chaos. Several simple and useful
characterizations of this notion of chaos in the setting of linear dynamics were obtained …

We study the spaceability of the set of recurrent vectors for an operator on a Banach space.
In particular, we find sufficient conditions for a quasi-rigid operator to have a recurrent …

We study dynamical notions lying between U U-frequent hypercyclicity and reiterative
hypercyclicity by investigating weighted upper densities between the unweighted upper …

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 …