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On transcendental meromorphic functions which are geometrically finite

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

Published online by Cambridge University Press:  09 April 2009

Jian-Hua Zheng
Jian-Hua Zheng
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China e-mail: [email protected]
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Abstract

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In this paper we give the definition of a meromorphic function which is geometrically finite and investigate some properties of geometrically finite meromorphic functions and the Lebesgue measure of their Julia sets.

Keywords

meromorphic functiongeometrically finiteJulia setLebesgue measure

MSC classification

Secondary: 37F10: Polynomials; rational maps; entire and meromorphic functions 37F50: Small divisors, rotation domains and linearization; Fatou and Julia sets 30D05: Functional equations in the complex domain, iteration and composition of analytic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 1 , February 2002 , pp. 93 - 108
Copyright
Copyright © Australian Mathematical Society 2002

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