Bernal-González, Luis; Montes-Rodríguez, Alfonso Universal functions for composition operators. (English) Zbl 0838.30032 Complex Variables, Theory Appl. 27, No. 1, 47-56 (1995). Let \(H(\Omega)\) be the space of analytic functions on a complex region \(\Omega\). In this paper, we characterize the sequences \(\{\varphi_n\}_{n\geq 1}\) of automorphisms of \(\Omega\) with the following property: There exists \(f\in H(\Omega)\) (in fact, a residual set of them) such that the orbit \(\{f\circ \varphi_n\}_{n\geq 1}\) is dense in \(H(\Omega)\). Some known results (as, for instance, Birkhoff’s theorem) are derived and some new others are obtained. Reviewer: L.Bernal-González (Sevilla) Cited in 2 ReviewsCited in 52 Documents MSC: 30E10 Approximation in the complex plane 47B38 Linear operators on function spaces (general) Keywords:universal function; automorphism region; run-away sequence; composition operator; residual set PDFBibTeX XMLCite \textit{L. Bernal-González} and \textit{A. Montes-Rodríguez}, Complex Variables, Theory Appl. 27, No. 1, 47--56 (1995; Zbl 0838.30032) Full Text: DOI