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Automatic differentiability and characterization of cocycles of holomorphic flows |
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| Authors: | Farhad Jafari Thomas Tonev Elena Toneva |
| Institution: | Department of Mathematics, University of Wyoming, Laramie, Wyoming 82071-3036 ; Department of Mathematical Sciences, University of Montana, Missoula, Montana 59812-1032 ; Department of Mathematics, 216 Kingston Hall, Eastern Washington University, Cheney, Washington 99004-2418 |
| 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. |
| Keywords: | Flow cocycle infinitesimal generator |
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