Document Type

Article

Publication Date

1-1-2005

Abstract

In this paper we prove that cocycles of holomorphic flows on domains in the complex plane are automatically differentiable with respect to the flow parameter, and their derivatives are holomorphic functions. We use this result to show that, on simply connected domains, an additive cocycle is a coboundary if and only if this cocycle vanishes at the fixed point of the flow.

Publication Title

Proceedings of the American Mathematical Society

DOI

10.1090/S0002-9939-05-07904-9

Comments

First published in Proceedings of the American Mathematical Society 133.11 (2005), published by the American Mathematical Society.

Included in

Mathematics Commons

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