科研之友
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摘要
We consider holomorphic maps f : U -> U for a hyperbolic domain U in the complex plane, such that the iterates of f converge to a boundary point zeta of U. By a previous result of the authors, for such maps there exist nice absorbing domains W subset of U. In this paper, we show that W can be chosen to be simply connected, if f has doubly parabolic type in the sense of the Baker-Pommerenke-Cowen classification of its lift by a universal covering (and zeta is not an isolated boundary point of U). We also provide counterexamples for other types of the map f, and give an exact characterization of doubly parabolic type in terms of the dynamical behaviour of f.
- 出版日期2015-8
