Remarks on Herman rings of transcendental meromorphic functions
Suppose that \(f\) is a meromorphic function whose inverse has only finitely many singular points. Following methods of \textit{A. Eremenko} and \textit{Yu. Lyubich} [Ann. Inst. Fourier 42, No. 4, 989-1020 (1992; Zbl 0735.58031)] it is shown that \(f\) has at most finitely many Herman rings. Using the construction of \textit{M. Shishikura} [Ann. Sci. Éc. Norm. Supér., IV. Sér. 20, 1-29 (1987; Zbl 0621.58030)] a meromorphic function is obtained which has infinitely many Herman rings.
scientific article; zbMATH DE number 1526418