ON THE ITERATION OF HOLOMORPHIC SELF-MAPS OF C

Authors
Citation
Lp. Fang, ON THE ITERATION OF HOLOMORPHIC SELF-MAPS OF C, Acta Mathematica Sinica, New Series, 14(1), 1998, pp. 139-144
Citations number
8
Categorie Soggetti
Mathematics,Mathematics,Mathematics,Mathematics
Journal title
Acta Mathematica Sinica, New Series
ISSN journal
10009574 → ACNP
Volume
14
Issue
1
Year of publication
1998
Pages
139 - 144
Database
ISI
SICI code
1000-9574(1998)14:1<139:OTIOHS>2.0.ZU;2-O
Abstract
Let f be a holomorphic self-map of the punctured plane C = C\{0} with essentially singular points 0 and infinity. In this note, we discuss the sets I-0(f) = {z is an element of C : f(n)(z) --> 0,n --> infinit y} and I-infinity(f) = {z is an element of C : f(n)(z) --> infinity,n --> infinity}.We try to find the relation between I-0(f),I-infinity(f ) and J(f). It is proved that both the boundary of I-0(f) and the boun dary of I-infinity(f) equal to J(f), I-0(f) boolean AND J(f) not equal 0 and I-infinity(f) boolean AND J(f) not equal 0. As a consequence of these results, we find both <(I-0(f))over bar> and I-infinity(f) are not doubly-bounded.