2021/11/09 by Stéphane Charpentier, Charpentier, Stéphane, Augustin Mouze +1
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV
paper · pdf · doi:10.48550/arxiv.2111.05165
arxiv created 2021/11/09 · openalex publication_date 2021/11/09 · arxiv updated 2021/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G and Ω be two planar domains. We give necessary and sufficient conditions on a sequence (ϕn) of eventually injective holomorphic mappings from G to Ω for the existence of a function f∈ H(Ω) whose orbit under the composition by (ϕn) is dense in H(G). This extends a result of the same nature obtained by Grosse-Erdmann and Mortini when G=Ω. An interconnexion between the topological properties of G and Ω appears. Further, in order to exhibit in a natural way holomorphic functions with wild boundary behaviour on planar domains, we study a certain type of universality for sequences of continuous mappings from a union of Jordan curves to a domain.