Details

Autor(en) / Beteiligte

• Barański, Krzysztof
• Fagella, Núria
• Jarque, Xavier
• Karpińska, Bogusława

Titel

Fatou components and singularities of meromorphic functions

Ist Teil von

• Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 2020-04, Vol.150 (2), p.633-654

Ort / Verlag

Cambridge: Cambridge University Press

Erscheinungsjahr

2020

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Abstract We prove several results concerning the relative position of points in the postsingular set P ( f ) of a meromorphic map f and the boundary of a Baker domain or the successive iterates of a wandering component. For Baker domains we answer a question of Mihaljević-Brandt and Rempe-Gillen. For wandering domains we show that if the iterates U n of such a domain have uniformly bounded diameter, then there exists a sequence of postsingular values p n such that ${\rm dist} (p_n, U_n)\to 0$ as $n\to \infty $ . We also prove that if $U_n \cap P(f)=\emptyset $ and the postsingular set of f lies at a positive distance from the Julia set (in ℂ), then the sequence of iterates of any wandering domain must contain arbitrarily large disks. This allows to exclude the existence of wandering domains for some meromorphic maps with infinitely many poles and unbounded set of singular values.