2012/11/03 by Tarakanta Nayak, Nayak, Tarakanta
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37F10 #Secondary 37F45 #math.DS #msc:37F10 #msc:37F45
paper · pdf · doi:10.48550/arxiv.1211.0600
12 pages
arxiv created 2015/01/07 · arxiv updated 2015/01/08
We investigate the existence and distribution of Herman rings of transcendental meromorphic functions which have at least one omitted value. If all the poles of such a function are multiple then it has no Herman ring. Herman rings of period one or two do not exist. Functions with a single pole or with at least two poles one of which is an omitted value have no Herman ring. Every doubly connected periodic Fatou component is a Herman ring.