On Quasi-nested wandering domains

Abstract

In this paper, the nature of the singularity of a meromorphic functions of the form f (z) = 1 h(z) + a for a ? C and h is an entire function having a Baker wandering domain, lying over the Baker omitted value is discussed. Various dynamical issues relating to the singular values of f have been studied. Also following are shown in this paper. If a be the Baker omitted value of f then f has a Quasi-nested wandering domain U if and only if there exists {nk}k>0 such that each Unk surrounds a and Unk ? a as k ? ?. If f is a function having Quasi-nested wandering domain then all the Fatou components of f are bounded. In particular, f has no Baker domain. Also existence of Quasi-nested wandering domain ensures that the Julia component containing ? i.e., J? is a singleton buried component. At the end of the paper a result about the non existence of Quasi-nested wandering domain is given.