2018/06/19 by Blas M. Caraballo, Caraballo, Blas M., Vinícius V. Fávaro +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Geometry and complex manifolds #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1806.07413
openalex publication_date 2018/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A classical result of Godefroy and Shapiro states that every nontrivial convolution operator on the space H(ℂn) of entire functions of several complex variables is hypercyclic. In sharp contrast with this result Fávaro and Mujica show that no translation operator on the space H(ℂ^ℕ) of entire functions of infinitely many complex variables is hypercyclic. In this work we study the linear dynamics of convolution operators on H(ℂ^ℕ). First we show that no convolution operator on H(ℂ^ℕ) is neither cyclic nor n-supercyclic for any positive integer n. After we study the notion of Li--Yorke chaos in non-metrizable topological vector spaces and we show that every nontrivial convolution operator on H(ℂ^ℕ) is Li--Yorke chaotic.