We shall show that for certain holomorphic maps, all Fatou components are simply connected. We also discuss the relation between wandering domains and singularities for certain meromorphic maps.

For a polynomial P it is well known that its Julia set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\cal J_P}$\end{document} is connected if and only if the orbits o...

Let U be a Baker domain of a transcendental entire function f. Denote by λU the hyperbolic metric in U and, for w ∈ U and n ∈ ℕ, define ρn(w) = λ U(fn+1}(w),fn(w)) and ρ(w) = limn→∞ρn(w). Here fn denotes the n-th iterate of f. It is shown that if the set of singularities of f− 1 that are contained in U is bounded, then \documentclass[12pt]{minimal}...