Normality and attracting fixed points

Jianming Chang, Mingliang Fang, Lawrence Zalcman

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)777-788
Number of pages12
JournalBulletin of the London Mathematical Society
Volume40
Issue number5
DOIs
StatePublished - Oct 2008

Bibliographical note

Funding Information:
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.

Funding

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.

FundersFunder number
Fred and Barbara Kort Sino–Israel Post Doctoral Fellowship Program at Bar-Ilan University
German-Israeli Foundation for Scientific Research and DevelopmentG-809-234.6/2003
National Natural Science Foundation of China10771076, 10671093

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