EXISTENCE OF HERMAN RINGS FOR MEROMORPHIC FUNCTIONS

Nuria Fagella and Patricia Dominguez

Departament de Matematica aplicada i Analisi
Universitat de Barcelona
Gran Via 585
08005 Barcelona
Spain
e-mail: fagella@maia.ub.es, patricia@maia.ub.es

ABSTRACT:

We apply the Shishikura surgery construction to transcendental 
maps in order to obtain examples of meromorphic functions with 
Herman rings, in a variety of possible arrangements. We give a 
sharp bound on the maximum possible number of such rings that 
a meromorphic function may have, in terms of the number of poles. 
Finally we discuss the possibility of having ``unbounded'' Herman 
rings (i.e., with an essential singularity in the boundary), 
and give some examples of maps with this property.