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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)



Normality and repelling periodic points

Authors: Jianming Chang and Lawrence Zalcman
Journal: Trans. Amer. Math. Soc. 363 (2011), 5721-5744
MSC (2000): Primary 30D45, 30D05, 37F10, 37C25
Published electronically: June 17, 2011
MathSciNet review: 2817406
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ k\ge 3(\ge 2)$ be an integer and $ \mathcal{F}$ be a family of functions meromorphic in a domain $ D\subset\mathbb{C}$, all of whose poles have multiplicity at least 2 (at least 3). If in $ D$ each $ f\in\mathcal{F}$ has neither repelling fixed points nor repelling periodic points of period $ k$, then $ \mathcal{F}$ is a normal family in $ D$. Examples are given to show that the conditions on poles are necessary and sharp.

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Additional Information

Jianming Chang
Affiliation: Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, People’s Republic of China

Lawrence Zalcman
Affiliation: Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel

Keywords: Meromorphic function, normal family, iterate, fixed point, periodic point.
Received by editor(s): September 6, 2009
Published electronically: June 17, 2011
Additional Notes: The research of the first author was supported by NNSF of China (Grant No. 10871094), NSFU of Jiangsu, China (Grant No. 08KJB110001), Qinglan Project of Jiangsu, China, and the SRF for ROCS, SEM.
The research of the second author was supported by Israel Science Foundation Grant 395/07. This work is part of the European Science Foundation Networking Programme HCAA.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.