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arXiv · 1211.0600

Herman rings of meromorphic maps with an omitted value

Tarakanta Nayak
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Abstract

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.

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Tarakanta Nayak. 2015-01-07. Herman rings of meromorphic maps with an omitted value. https://arxiv.org/abs/1211.0600

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