arXiv:1211.0600 Abstract | arXiv Analytics

arXiv:1211.0600 [math.DS]Abstract References Reviews Resources

Herman rings of meromorphic maps with an omitted value

Published 2012-11-03, updated 2015-01-07Version 2

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.

Comments: 12 pages

Categories: math.DS

Subjects: 37F10, 37F45

Keywords: herman ring, omitted value, meromorphic maps, doubly connected periodic fatou component, meromorphic functions

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