We show that the bilateral backward shift on ℓ p (Z, ω) that has a projective orbit with a non-
zero limit point is supercyclic. This phenomenon holds also for Γ-supercyclicity, which …

We study frequently recurrent unilateral and bilateral backward shift operators on Fr\'echet
sequence spaces. We prove that if a backward shift admits a non-zero frequently recurrent …

Let ω be a weight function defined on a locally compact group G, 1⩽ p<+∞, S⊂ G and let us
assume that for any s∈ S, the left translation operator T s is continuous from the weighted L …

We characterize the subsets Γ Γ of the complex plane CC for which the notion of Γ Γ-
supercyclicity for strongly continuous semigroups coincides with that of hypercyclicity. In …

Given a Furstenberg family F and a subset {\Gamma} of C, we introduce and explore the
notions of F_ {\Gamma}-hypercyclic operator and F-hypercyclic scalar set. First, the study of …

This paper explores the notions of $\mathcal {F} $-transitivity and topological $\mathcal {F} $-
recurrence for backward shift operators on weighted $\ell^ p $-spaces and $ c_0 $-spaces …

We characterize the Γ-supercyclicity of bilateral shift operators and translation semigroups in
weighted Lp spaces in terms of the weight and Γ. We survey the notion of S-density …

We completely characterize the finite-dimensional subsets C of any separable Hilbert space
for which the notion of C-hypercyclicity coincides with the notion of hypercyclicity, where an …

We study the dynamics induced by homogeneous polynomials on Banach spaces. It is
known that no homogeneous polynomial defined on a Banach space can have a dense …

In this article we discuss an interesting idea related to characte rization of diskcyclicity
phenomena. We use the Diskcyclic Crit erion to characterize the subsets Γ of ℂ for which the …