Is the process of finding f′ chaotic?

Abstract

Let (H (C) , ρ) be the metric space of all entire functions f where the metric ρ induces the topology of uniform convergence on compact subsets of the complex plane. Let D : H (C) → H (C) be the linear mapping that assigns to each f its derivative, D(f) = f′ . We show in this note that the set of entire functions that are periodic under this map is dense in (H (C) , ρ). It implies that D : H (C) → H (C) is chaotic in the sense of Devaney.

Keywords

• Entire functions
• chaotic maps