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Hyperbolic Metric and Multiply Connected Wandering Domains of Meromorphic Functions

Part of: Entire and meromorphic functions, and related topics Complex dynamical systems

Published online by Cambridge University Press:  30 January 2017

Jian-Hua Zheng
Jian-Hua Zheng*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China ([email protected])
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Abstract

In this paper, in terms of the hyperbolic metric, we give a condition under which the image of a hyperbolic domain of an analytic function contains a round annulus centred at the origin. From this, we establish results on the multiply connected wandering domains of a meromorphic function that contain large round annuli centred at the origin. We thereby successfully extend the results of transcendental meromorphic functions with finitely many poles to those with infinitely many poles.

Keywords

wandering domainhyperbolic metricannulus domainsFatou setJulia set

MSC classification

Secondary: 37F10: Polynomials; rational maps; entire and meromorphic functions 30D05: Functional equations in the complex domain, iteration and composition of analytic functions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 3 , August 2017 , pp. 787 - 810
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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