4 papers · 1 filter
Existence of hypercyclic algebras in Fréchet algebras
Fernando Costa, Álvaro Rocha
We prove that every separable infinite-dimensional Fréchet algebra admits a continuous linear operator supporting a dense invariant hypercyclic algebra, giving an affirmati…
Self-similar fractals and common hypercyclicity
Fernando Costa
We obtain a multi-dimensional generalization of the Costakis-Sambarino criterion for common hypercyclic vectors with optimal consequences on a large class of fractals. Applications…
Common hypercyclic algebras for families of products of backward shifts
Fernando Costa
In this paper, we generalize to the context of algebras some recent results on the existence of common hypercyclic vectors for families of products of backward shift operators. We…
Common hypercyclic vectors and dimension of the parameter set
Frédéric Bayart, Fernando Costa, Quentin Menet
We investigate the existence of a common hypercyclic vector for a family of hypercyclicoperators acting on the same Banach space . We give positive and negative…