Singularities and wandering domains in iteration of meromorphic functions

Authors
Citation
Jh. Zheng, Singularities and wandering domains in iteration of meromorphic functions, ILL J MATH, 44(3), 2000, pp. 520-530
Citations number
20
Categorie Soggetti
Mathematics
Journal title
ILLINOIS JOURNAL OF MATHEMATICS
ISSN journal
00192082 → ACNP
Volume
44
Issue
3
Year of publication
2000
Pages
520 - 530
Database
ISI
SICI code
0019-2082(200023)44:3<520:SAWDII>2.0.ZU;2-K
Abstract
Let f be a transcendental meromorphic function and let LI be a wandering do main of f. Under some conditions, we prove that a finite limit function of {f(n)} on U is in the derived set of the forward orbit of the set sing (f(- 1)) of singularities of the inverse function of f. The existence of {n(k)} such that f(nk)\u tends to infinity is also considered when f is entire. If sing(f(-1)) is bounded, however, we show that {f(n)(z)}(n=0)(infinity) in F(f) does not tend to infinity.