摘要
All possible arrangements of cycles of three periodic as well as four periodicHerman rings of transcendental meromorphic functions having at least one omitted value aredetermined. It is shown that if p = 3 or 4, then the number of p-cycles of Herman rings isat most one. We have also proved a result about the non-existence of a 3-cycle and a 4-cycleof Herman rings simultaneously. Finally some examples of functions having no Herman ringare discussed.
All possible arrangements of cycles of three periodic as well as four periodicHerman rings of transcendental meromorphic functions having at least one omitted value aredetermined. It is shown that if p = 3 or 4, then the number of p-cycles of Herman rings isat most one. We have also proved a result about the non-existence of a 3-cycle and a 4-cycleof Herman rings simultaneously. Finally some examples of functions having no Herman ringare discussed.
基金
supported by CSIR
Department of Science and Technology,Goverment of India through a Fast Track Project(SR-FTP-MS019-2011)respectively
