Common hypercyclic vectors and dimension of the parameter set

2021/03/24 by Bayart, Frédéric, Costa, Fernando, Menet, Quentin
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2103.13152

Abstract

We investigate the existence of a common hypercyclic vector for a family (T_λ)_{λ∈ Λ} of hypercyclicoperators acting on the same Banach space X. We give positive and negative results involving the dimension of Λ and the regularity of each map λ∈ Λ↦ T_λⁿ x, x∈ X, n∈\mathbb N.

Related

• Common hypercyclic vectors for high dimensional families of operators
• Common hypercyclic vectors for composition operators
• Common hypercyclic vectors for multiples of backward shift
• Common upper frequent hypercyclicity
• Existence of common hypercyclic vectors for translation operators