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Bulletin of the London Mathematical Society Advance Access originally published online on July 3, 2008
Bulletin of the London Mathematical Society 2008 40(5):777-788; doi:10.1112/blms/bdn056
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© 2008 London Mathematical Society

Normality and attracting fixed points

Jianming Chang

Department of Mathematics
Changshu Institute of Technology
Changshu
Jiangsu 215500
P. R. China
jmwchang@pub.sz.jsinfo.net

Mingliang Fang

Institute of Applied Mathematics
South China Agricultural University
Guangzhou 510642
P. R. China
hnmlfang@hotmail.com

Lawrence Zalcman

Department of Mathematics
Bar-Ilan University
52900 Ramat-Gan
Israel

Received 11 September 2007. Revision received 12 March 2008.

Let k ≥ 2 be a fixed integer. We construct a non-normal family of meromorphic functions in the unit disc with kth iterates that have no non-attracting fixed points in the unit disc. We also prove that a family of meromorphic functions in a plane domain is normal if all fixed points in the domain of the k-iterates of all functions in the family are uniformly attracting.

2000 Mathematics Subject Classification 30D45, 37F10, 37C25.

The first author is supported by the Fred and Barbara Kort Sino-Israel Post Doctoral Fellowship Program at Bar-Ilan University, and the NNSF of China (grant no. 10671093). The second author is supported by the NNSF of China (grant no. 10771076), and the second and third authors are supported by the German-Israeli Foundation for Scientific Research and Development, grant G-809-234.6/2003.


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