Rotation domains and stable Baker omitted value (Q2239837)

A Baker omitted value \(v\) of a transcendental meromorphic function \(f\) is an omitted value such that there is a disk \(D\) centered at the \(v\) for which each component of the boundary of \(f^{-1}(D)\) is bounded. This paper focuses on several results about meromorphic functions for which all iterations are well defined at the Baker omitted value. In particular, it is proved that: \begin{itemize} \item[1.] The number of \(p\)-periodic Herman rings is finite for each \(p\geq 1\); \item[2.] Every Julia component intersects the boundaries of at most finitely many Herman rings; \item[3.] Under certain technical conditions, such as the Baker omitted value is the only limit point of critical value, and the number of critical points corresponding to each critical value lying in the Julia set is finite, the accumulation point of a Julia component is either a parabolic period point or in the \(\omega\)-limit point of recurrent critical points, and the the boundary of rotation domains is the \(\omega\)-limit point of recurrent critical points. \end{itemize}