Periodic points and normal families

Citation
D. Bargmann et W. Bergweiler, Periodic points and normal families, P AM MATH S, 129(10), 2001, pp. 2881-2888
Citations number
19
Categorie Soggetti
Mathematics
Journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029939 → ACNP
Volume
129
Issue
10
Year of publication
2001
Pages
2881 - 2888
Database
ISI
SICI code
0002-9939(2001)129:10<2881:PPANF>2.0.ZU;2-M
Abstract
Let F be the family of all functions which are holomorphic in some domain a nd do not have periodic points of some period greater than one there. It is shown that F is quasinormal, and the sequences in F which do not have conv ergent subsequences are characterized. The method also yields a new proof o f the result that transcendental entire functions have infinitely many peri odic points of all periods greater than one.