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 language | English |
|---|---|
| Pages (from-to) | 777-788 |
| Number of pages | 12 |
| Journal | Bulletin of the London Mathematical Society |
| Volume | 40 |
| Issue number | 5 |
| DOIs | |
| State | Published - 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.
| Funders | Funder number |
|---|---|
| Fred and Barbara Kort Sino–Israel Post Doctoral Fellowship Program at Bar-Ilan University | |
| German-Israeli Foundation for Scientific Research and Development | G-809-234.6/2003 |
| National Natural Science Foundation of China | 10771076, 10671093 |