Journal of Mathematics of Kyoto University

Non-existence of unbounded Fatou components of a meromorphic function

Jian-Hua Zheng and Piyapong Niamsup

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This paper is devoted to study of sufficient conditions under which a transcendental meromorphic function has no unbounded Fatou components and to extension of some results for entire functions to meromorphic functions. Actually, we shall mainly discuss non-existence of unbounded wandering domains of a meromorphic function. The case for a composition of finitely many meromorphic functions with at least one of them being transcendental can be also investigated in terms of the argument of this paper.

Article information

J. Math. Kyoto Univ., Volume 49, Number 1 (2009), 1-12.

First available in Project Euclid: 30 July 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37F10: Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]
Secondary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX]


Zheng, Jian-Hua; Niamsup, Piyapong. Non-existence of unbounded Fatou components of a meromorphic function. J. Math. Kyoto Univ. 49 (2009), no. 1, 1--12. doi:10.1215/kjm/1248983027.

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